This namespace is used for special functions that in GSL are prefixed gsl_sf. More...

Namespaces
namespace	airy
	Namespace for Airy functions.

namespace	bessel
	Namespace for Bessel functions.

namespace	coulomb
	Namespace for `gsl_sf_coulomb` functions.

namespace	ellint
	Namespace for elliptic integrals.

namespace	hermite
	Namespace for physicist Hermite polynomials.

namespace	lambert
	Lambert functions.

namespace	legendre
	Legendre functions.

namespace	mathieu
	Angular and radial Mathieu functions.

Typedefs
typedef gsl_sf_result	result
	Typedef for `gsl_sf_result`. More...

typedef gsl_sf_result_e10	result_e10
	Typedef for `gsl_sf_result_e10`. More...

Functions
int	clausen_e (double const x, result &result)
	C++ version of gsl_sf_clausen(). More...

double	clausen (double const x)
	C++ version of gsl_sf_clausen(). More...

int	hydrogenicR_1_e (double const Z, double const r, result &result)
	C++ version of gsl_sf_hydrogenicR_1(). More...

double	hydrogenicR_1 (double const Z, double const r)
	C++ version of gsl_sf_hydrogenicR_1(). More...

int	hydrogenicR_e (int const n, int const l, double const Z, double const r, result &result)
	C++ version of gsl_sf_hydrogenicR_e(). More...

double	hydrogenicR (int const n, int const l, double const Z, double const r)
	C++ version of gsl_sf_hydrogenicR(). More...

int	coupling_3j_e (int two_ja, int two_jb, int two_jc, int two_ma, int two_mb, int two_mc, result &result)
	C++ version of gsl_sf_coupling_3j(). More...

double	coupling_3j (int two_ja, int two_jb, int two_jc, int two_ma, int two_mb, int two_mc)
	C++ version of gsl_sf_coupling_3j(). More...

int	coupling_6j_e (int two_ja, int two_jb, int two_jc, int two_jd, int two_je, int two_jf, result &result)
	C++ version of gsl_sf_coupling_6j_e(). More...

double	coupling_6j (int two_ja, int two_jb, int two_jc, int two_jd, int two_je, int two_jf)
	C++ version of gsl_sf_coupling_6j(). More...

int	coupling_RacahW_e (int two_ja, int two_jb, int two_jc, int two_jd, int two_je, int two_jf, result &result)
	C++ version of gsl_sf_coupling_RacahW_e(). More...

double	coupling_RacahW (int two_ja, int two_jb, int two_jc, int two_jd, int two_je, int two_jf)
	C++ version of gsl_sf_coupling_RacahW(). More...

int	coupling_9j_e (int two_ja, int two_jb, int two_jc, int two_jd, int two_je, int two_jf, int two_jg, int two_jh, int two_ji, result &result)
	C++ version of gsl_sf_coupling_9j_e(). More...

double	coupling_9j (int two_ja, int two_jb, int two_jc, int two_jd, int two_je, int two_jf, int two_jg, int two_jh, int two_ji)
	C++ version of gsl_sf_coupling_9j(). More...

int	dawson_e (double x, result &result)
	C++ version of gsl_sf_dawson_e(). More...

double	dawson (double x)
	C++ version of gsl_sf_dawson(). More...

int	debye_1_e (double const x, result &result)
	C++ version of gsl_sf_debye_1_e(). More...

double	debye_1 (double const x)
	C++ version of gsl_sf_debye_1(). More...

int	debye_2_e (double const x, result &result)
	C++ version of gsl_sf_debye_2_e(). More...

double	debye_2 (double const x)
	C++ version of gsl_sf_debye_2(). More...

int	debye_3_e (double const x, result &result)
	C++ version of gsl_sf_debye_3_e(). More...

double	debye_3 (double const x)
	C++ version of gsl_sf_debye_3(). More...

int	debye_4_e (double const x, result &result)
	C++ version of gsl_sf_debye_4_e(). More...

double	debye_4 (double const x)
	C++ version of gsl_sf_debye_4(). More...

int	debye_5_e (double const x, result &result)
	C++ version of gsl_sf_debye_5_e(). More...

double	debye_5 (double const x)
	C++ version of gsl_sf_debye_5(). More...

int	debye_6_e (double const x, result &result)
	C++ version of gsl_sf_debye_6_e(). More...

double	debye_6 (double const x)
	C++ version of gsl_sf_debye_6(). More...

int	dilog_e (double x, result &result)
	C++ version of gsl_sf_dilog(). More...

double	dilog (double const x)
	C++ version of gsl_sf_dilog(). More...

int	complex_dilog_xy_e (double const x, double const y, result &result_re, result &result_im)
	C++ version of gsl_sf_complex_dilog_xy_e(). More...

int	complex_dilog_e (double const r, double const theta, result &result_re, result &result_im)
	C++ version of gsl_sf_complex_dilog_e(). More...

int	complex_spence_xy_e (double const x, double const y, result &real_sp, result &imag_sp)
	C++ version of gsl_sf_complex_spence_xy_e(). More...

int	multiply_e (double const x, double const y, result &result)
	C++ version of gsl_sf_multiply_e(). More...

double	multiply (double const x, double const y)
	C++ version of gsl_sf_multiply(). More...

int	multiply_err_e (double const x, double const dx, double const y, double const dy, result &result)
	C++ version of gsl_sf_multiply_err_e(). More...

int	elljac_e (double const u, double const m, double &sn, double &cn, double &dn)
	C++ version of gsl_sf_elljac_e(). More...

int	erfc_e (double x, result &result)
	C++ version of gsl_sf_erfc_e(). More...

double	erfc (double x)
	C++ version of gsl_sf_erfc(). More...

int	log_erfc_e (double x, result &result)
	C++ version of gsl_sf_log_erfc_e(). More...

double	log_erfc (double x)
	C++ version of gsl_sf_log_erfc(). More...

int	erf_e (double x, result &result)
	C++ version of gsl_sf_erf_e(). More...

double	erf (double x)
	C++ version of gsl_sf_erf(). More...

int	erf_Z_e (double x, result &result)
	C++ version of gsl_sf_erf_Z_e(). More...

int	erf_Q_e (double x, result &result)
	C++ version of gsl_sf_erf_Q_e(). More...

double	erf_Z (double x)
	C++ version of gsl_sf_erf_Z(). More...

double	erf_Q (double x)
	C++ version of gsl_sf_erf_Q(). More...

int	hazard_e (double x, result &result)
	C++ version of gsl_sf_hazard_e(). More...

double	hazard (double x)
	C++ version of gsl_sf_hazard(). More...

int	exp_e (double x, result &result)
	C++ version of gsl_sf_exp_e(). More...

double	exp (double const x)
	C++ version of gsl_sf_exp(). More...

int	exp_e10_e (double const x, result_e10 &result)
	C++ version of gsl_sf_exp_e10_e(). More...

int	exp_mult_e (double const x, double const y, result &result)
	C++ version of gsl_sf_exp_mult_e(). More...

double	exp_mult (double const x, double const y)
	C++ version of gsl_sf_exp_mult(). More...

int	exp_mult_e10_e (double const x, double const y, result_e10 &result)
	C++ version of gsl_sf_exp_mult_e10_e(). More...

int	expm1_e (double const x, result &result)
	C++ version of gsl_sf_expm1_e(). More...

double	expm1 (double const x)
	C++ version of gsl_sf_expm1(). More...

int	exprel_e (double const x, result &result)
	C++ version of gsl_sf_exprel_e(). More...

double	exprel (double const x)
	C++ version of gsl_sf_exprel(). More...

int	exprel_2_e (double x, result &result)
	C++ version of gsl_sf_exprel_2_e(). More...

double	exprel_2 (double const x)
	C++ version of gsl_sf_exprel_2(). More...

int	exprel_n_e (int const n, double const x, result &result)
	C++ version of gsl_sf_exprel_n_e(). More...

double	exprel_n (int const n, double const x)
	C++ version of gsl_sf_exprel_n(). More...

int	exprel_n_CF_e (double const n, double const x, result &result)
	C++ version of gsl_sf_exprel_n_CF_e(). More...

int	exp_err_e (double const x, double const dx, result &result)
	C++ version of gsl_sf_exp_err_e(). More...

int	exp_err_e10_e (double const x, double const dx, result_e10 &result)
	C++ version of gsl_sf_exp_err_e10_e(). More...

int	exp_mult_err_e (double const x, double const dx, double const y, double const dy, result &result)
	C++ version of gsl_sf_exp_mult_err_e(). More...

int	exp_mult_err_e10_e (double const x, double const dx, double const y, double const dy, result_e10 &result)
	C++ version of gsl_sf_exp_mult_err_e10_e(). More...

int	expint_E1_e (double x, result &result)
	C++ version of gsl_sf_expint_E1_e(). More...

double	expint_E1 (double const x)
	C++ version of gsl_sf_expint_E1(). More...

int	expint_E2_e (double const x, result &result)
	C++ version of gsl_sf_expint_E2_e(). More...

double	expint_E2 (double const x)
	C++ version of gsl_sf_expint_E2(). More...

int	expint_En_e (int const n, double const x, result &result)
	C++ version of gsl_sf_expint_En_e(). More...

double	expint_En (int const n, double const x)
	C++ version of gsl_sf_expint_En(). More...

int	expint_E1_scaled_e (double const x, result &result)
	C++ version of gsl_sf_expint_E1_scaled_e(). More...

double	expint_E1_scaled (double const x)
	C++ version of gsl_sf_expint_E1_scaled(). More...

int	expint_E2_scaled_e (double const x, result &result)
	C++ version of gsl_sf_expint_E2_scaled_e(). More...

double	expint_E2_scaled (double const x)
	C++ version of gsl_sf_expint_E2_scaled(). More...

int	expint_En_scaled_e (int const n, double const x, result &result)
	C++ version of gsl_sf_expint_En_scaled_e(). More...

double	expint_En_scaled (int const n, double const x)
	C++ version of gsl_sf_expint_En_scaled(). More...

int	expint_Ei_e (double const x, result &result)
	C++ version of gsl_sf_expint_Ei_e(). More...

double	expint_Ei (double const x)
	C++ version of gsl_sf_expint_Ei(). More...

int	expint_Ei_scaled_e (double const x, result &result)
	C++ version of gsl_sf_expint_Ei_scaled_e(). More...

double	expint_Ei_scaled (double const x)
	C++ version of gsl_sf_expint_Ei_scaled(). More...

int	Shi_e (double const x, result &result)
	C++ version of gsl_sf_Shi_e(). More...

double	Shi (double const x)
	C++ version of gsl_sf_Shi(). More...

int	Chi_e (double const x, result &result)
	C++ version of gsl_sf_Chi_e(). More...

double	Chi (double const x)
	C++ version of gsl_sf_Chi(). More...

int	expint_3_e (double const x, result &result)
	C++ version of gsl_sf_expint_3_e(). More...

double	expint_3 (double x)
	C++ version of gsl_sf_expint_3(). More...

int	Si_e (double const x, result &result)
	C++ version of gsl_sf_Si_e(). More...

double	Si (double const x)
	C++ version of gsl_sf_Si(). More...

int	Ci_e (double const x, result &result)
	C++ version of gsl_sf_Ci_e(). More...

double	Ci (double const x)
	C++ version of gsl_sf_Ci(). More...

int	atanint_e (double const x, result &result)
	C++ version of gsl_sf_atanint_e(). More...

double	atanint (double const x)
	C++ version of gsl_sf_atanint(). More...

int	fermi_dirac_m1_e (double const x, result &result)
	C++ version of gsl_sf_fermi_dirac_m1_e(). More...

double	fermi_dirac_m1 (double const x)
	C++ version of gsl_sf_fermi_dirac_m1(). More...

int	fermi_dirac_0_e (double const x, result &result)
	C++ version of gsl_sf_fermi_dirac_0_e(). More...

double	fermi_dirac_0 (double const x)
	C++ version of gsl_sf_fermi_dirac_0(). More...

int	fermi_dirac_1_e (double const x, result &result)
	C++ version of gsl_sf_fermi_dirac_1_e(). More...

double	fermi_dirac_1 (double const x)
	C++ version of gsl_sf_fermi_dirac_1(). More...

int	fermi_dirac_2_e (double const x, result &result)
	C++ version of gsl_sf_fermi_dirac_2_e(). More...

double	fermi_dirac_2 (double const x)
	C++ version of gsl_sf_fermi_dirac_2(). More...

int	fermi_dirac_int_e (int const j, double const x, result &result)
	C++ version of gsl_sf_fermi_dirac_int_e(). More...

double	fermi_dirac_int (int const j, double const x)
	C++ version of gsl_sf_fermi_dirac_int(). More...

int	fermi_dirac_mhalf_e (double const x, result &result)
	C++ version of gsl_sf_fermi_dirac_mhalf_e(). More...

double	fermi_dirac_mhalf (double const x)
	C++ version of gsl_sf_fermi_dirac_mhalf(). More...

int	fermi_dirac_half_e (double const x, result &result)
	C++ version of gsl_sf_fermi_dirac_half_e(). More...

double	fermi_dirac_half (double const x)
	C++ version of gsl_sf_fermi_dirac_half(). More...

int	fermi_dirac_3half_e (double const x, result &result)
	C++ version of gsl_sf_fermi_dirac_3half_e(). More...

double	fermi_dirac_3half (double const x)
	C++ version of gsl_sf_fermi_dirac_3half(). More...

int	fermi_dirac_inc_0_e (double const x, double const b, result &result)
	C++ version of gsl_sf_fermi_dirac_inc_0_e(). More...

double	fermi_dirac_inc_0 (double const x, double const b)
	C++ version of gsl_sf_fermi_dirac_inc_0(). More...

int	lngamma_e (double x, result &result)
	C++ version of gsl_sf_lngamma_e(). More...

double	lngamma (double const x)
	C++ version of gsl_sf_lngamma(). More...

int	lngamma_sgn_e (double x, result &result_lg, double &sgn)
	C++ version of gsl_sf_lngamma_sgn_e(). More...

int	gamma_e (double const x, result &result)
	C++ version of gsl_sf_gamma_e(). More...

double	gamma (double const x)
	C++ version of gsl_sf_gamma(). More...

int	gammastar_e (double const x, result &result)
	C++ version of gsl_sf_gammastar_e(). More...

double	gammastar (double const x)
	C++ version of gsl_sf_gammastar(). More...

int	gammainv_e (double const x, result &result)
	C++ version of gsl_sf_gammainv_e(). More...

double	gammainv (double const x)
	C++ version of gsl_sf_gammainv(). More...

int	lngamma_complex_e (double zr, double zi, result &lnr, result &arg)
	C++ version of gsl_sf_lngamma_complex_e(). More...

int	taylorcoeff_e (int const n, double const x, result &result)
	C++ version of gsl_sf_taylorcoeff_e(). More...

double	taylorcoeff (int const n, double const x)
	C++ version of gsl_sf_taylorcoeff(). More...

int	fact_e (unsigned int const n, result &result)
	C++ version of gsl_sf_fact_e(). More...

double	fact (unsigned int const n)
	C++ version of gsl_sf_fact(). More...

int	doublefact_e (unsigned int const n, result &result)
	C++ version of gsl_sf_doublefact_e(). More...

double	doublefact (unsigned int const n)
	C++ version of gsl_sf_doublefact(). More...

int	lnfact_e (unsigned int const n, result &result)
	C++ version of gsl_sf_lnfact_e(). More...

double	lnfact (unsigned int const n)
	C++ version of gsl_sf_lnfact(). More...

int	lndoublefact_e (unsigned int const n, result &result)
	C++ version of gsl_sf_lndoublefact_e(). More...

double	lndoublefact (unsigned int const n)
	C++ version of gsl_sf_lndoublefact(). More...

int	lnchoose_e (unsigned int n, unsigned int m, result &result)
	C++ version of gsl_sf_lnchoose_e(). More...

double	lnchoose (unsigned int n, unsigned int m)
	C++ version of gsl_sf_lnchoose(). More...

int	choose_e (unsigned int n, unsigned int m, result &result)
	C++ version of gsl_sf_choose_e(). More...

double	choose (unsigned int n, unsigned int m)
	C++ version of gsl_sf_choose(). More...

int	lnpoch_e (double const a, double const x, result &result)
	C++ version of gsl_sf_lnpoch_e(). More...

double	lnpoch (double const a, double const x)
	C++ version of gsl_sf_lnpoch(). More...

int	lnpoch_sgn_e (double const a, double const x, result &result, double &sgn)
	C++ version of gsl_sf_lnpoch_sgn_e(). More...

int	poch_e (double const a, double const x, result &result)
	C++ version of gsl_sf_poch_e(). More...

double	poch (double const a, double const x)
	C++ version of gsl_sf_poch(). More...

int	pochrel_e (double const a, double const x, result &result)
	C++ version of gsl_sf_pochrel_e(). More...

double	pochrel (double const a, double const x)
	C++ version of gsl_sf_pochrel(). More...

int	gamma_inc_Q_e (double const a, double const x, result &result)
	C++ version of gsl_sf_gamma_inc_Q_e(). More...

double	gamma_inc_Q (double const a, double const x)
	C++ version of gsl_sf_gamma_inc_Q(). More...

int	gamma_inc_P_e (double const a, double const x, result &result)
	C++ version of gsl_sf_gamma_inc_P_e(). More...

double	gamma_inc_P (double const a, double const x)
	C++ version of gsl_sf_gamma_inc_P(). More...

int	gamma_inc_e (double const a, double const x, result &result)
	C++ version of gsl_sf_gamma_inc_e(). More...

double	gamma_inc (double const a, double const x)
	C++ version of gsl_sf_gamma_inc(). More...

int	lnbeta_e (double const a, double const b, result &result)
	C++ version of gsl_sf_lnbeta_e(). More...

double	lnbeta (double const a, double const b)
	C++ version of gsl_sf_lnbeta(). More...

int	lnbeta_sgn_e (double const x, double const y, result &result, double &sgn)
	C++ version of gsl_sf_lnbeta_sgn_e(). More...

int	beta_e (double const a, double const b, result &result)
	C++ version of gsl_sf_beta_e(). More...

double	beta (double const a, double const b)
	C++ version of gsl_sf_beta(). More...

int	beta_inc_e (double const a, double const b, double const x, result &result)
	C++ version of gsl_sf_beta_inc_e(). More...

double	beta_inc (double const a, double const b, double const x)
	C++ version of gsl_sf_beta_inc(). More...

int	gegenpoly_1_e (double lambda, double x, result &result)
	C++ version of gsl_sf_gegenpoly_1_e(). More...

int	gegenpoly_2_e (double lambda, double x, result &result)
	C++ version of gsl_sf_gegenpoly_2_e(). More...

int	gegenpoly_3_e (double lambda, double x, result &result)
	C++ version of gsl_sf_gegenpoly_3_e(). More...

double	gegenpoly_1 (double lambda, double x)
	C++ version of gsl_sf_gegenpoly_1(). More...

double	gegenpoly_2 (double lambda, double x)
	C++ version of gsl_sf_gegenpoly_2(). More...

double	gegenpoly_3 (double lambda, double x)
	C++ version of gsl_sf_gegenpoly_3(). More...

int	gegenpoly_n_e (int n, double lambda, double x, result &result)
	C++ version of gsl_sf_gegenpoly_n_e(). More...

double	gegenpoly_n (int n, double lambda, double x)
	C++ version of gsl_sf_gegenpoly_n(). More...

template<typename DATA >
int	gegenpoly_array (int nmax, double lambda, double x, DATA &result_array)
	C++ version of gsl_sf_gegenpoly_array(). More...

int	hyperg_0F1_e (double c, double x, result &result)
	C++ version of gsl_sf_hyperg_0F1_e(). More...

double	hyperg_0F1 (double const c, double const x)
	C++ version of gsl_sf_hyperg_0F1(). More...

int	hyperg_1F1_int_e (int const m, int const n, double const x, result &result)
	C++ version of gsl_sf_hyperg_1F1_int_e(). More...

double	hyperg_1F1_int (int const m, int const n, double x)
	C++ version of gsl_sf_hyperg_1F1_int(). More...

int	hyperg_1F1_e (double const a, double const b, double const x, result &result)
	C++ version of gsl_sf_hyperg_1F1_e(). More...

double	hyperg_1F1 (double a, double b, double x)
	C++ version of gsl_sf_hyperg_1F1(). More...

int	hyperg_U_int_e (int const m, int const n, double const x, result &result)
	C++ version of gsl_sf_hyperg_U_int_e(). More...

double	hyperg_U_int (int const m, int const n, double const x)
	C++ version of gsl_sf_hyperg_U_int(). More...

int	hyperg_U_int_e10_e (int const m, int const n, double const x, result_e10 &result)
	C++ version of gsl_sf_hyperg_U_int_e10_e(). More...

int	hyperg_U_e (double const a, double const b, double const x, result &result)
	C++ version of gsl_sf_hyperg_U_e(). More...

double	hyperg_U (double const a, double const b, double const x)
	C++ version of gsl_sf_hyperg_U(). More...

int	hyperg_U_e10_e (double const a, double const b, double const x, result_e10 &result)
	C++ version of gsl_sf_hyperg_U_e10_e(). More...

int	hyperg_2F1_e (double a, double b, double const c, double const x, result &result)
	C++ version of gsl_sf_hyperg_2F1_e(). More...

double	hyperg_2F1 (double a, double b, double c, double x)
	C++ version of gsl_sf_hyperg_2F1(). More...

int	hyperg_2F1_conj_e (double const aR, double const aI, double const c, double const x, result &result)
	C++ version of gsl_sf_hyperg_2F1_conj_e(). More...

double	hyperg_2F1_conj (double aR, double aI, double c, double x)
	C++ version of gsl_sf_hyperg_2F1_conj(). More...

int	hyperg_2F1_renorm_e (double const a, double const b, double const c, double const x, result &result)
	C++ version of gsl_sf_hyperg_2F1_renorm_e(). More...

double	hyperg_2F1_renorm (double a, double b, double c, double x)
	C++ version of gsl_sf_hyperg_2F1_renorm(). More...

int	hyperg_2F1_conj_renorm_e (double const aR, double const aI, double const c, double const x, result &result)
	C++ version of gsl_sf_hyperg_2F1_conj_renorm_e(). More...

double	hyperg_2F1_conj_renorm (double aR, double aI, double c, double x)
	C++ version of gsl_sf_hyperg_2F1_conj_renorm(). More...

int	hyperg_2F0_e (double const a, double const b, double const x, result &result)
	C++ version of gsl_sf_hyperg_2F0_e(). More...

double	hyperg_2F0 (double const a, double const b, double const x)
	C++ version of gsl_sf_hyperg_2F0(). More...

int	laguerre_1_e (double const a, double const x, result &result)
	C++ version of gsl_sf_laguerre_1_e(). More...

int	laguerre_2_e (double const a, double const x, result &result)
	C++ version of gsl_sf_laguerre_2_e(). More...

int	laguerre_3_e (double const a, double const x, result &result)
	C++ version of gsl_sf_laguerre_3_e(). More...

double	laguerre_1 (double a, double x)
	C++ version of gsl_sf_laguerre_1(). More...

double	laguerre_2 (double a, double x)
	C++ version of gsl_sf_laguerre_2(). More...

double	laguerre_3 (double a, double x)
	C++ version of gsl_sf_laguerre_3(). More...

int	laguerre_n_e (int const n, double const a, double const x, result &result)
	C++ version of gsl_sf_laguerre_n_e(). More...

double	laguerre_n (int n, double a, double x)
	C++ version of gsl_sf_laguerre_n(). More...

int	conicalP_half_e (double const lambda, double const x, result &result)

double	conicalP_half (double const lambda, double const x)
	C++ version of gsl_sf_conicalP_half(). More...

int	conicalP_mhalf_e (double const lambda, double const x, result &result)
	C++ version of gsl_sf_conicalP_mhalf_e(). More...

double	conicalP_mhalf (double const lambda, double const x)
	C++ version of gsl_sf_conicalP_mhalf(). More...

int	conicalP_0_e (double const lambda, double const x, result &result)
	C++ version of gsl_sf_conicalP_0_e(). More...

double	conicalP_0 (double const lambda, double const x)
	C++ version of gsl_sf_conicalP_0(). More...

int	conicalP_1_e (double const lambda, double const x, result &result)
	C++ version of gsl_sf_conicalP_1_e(). More...

double	conicalP_1 (double const lambda, double const x)
	C++ version of gsl_sf_conicalP_1(). More...

int	conicalP_sph_reg_e (int const l, double const lambda, double const x, result &result)
	C++ version of gsl_sf_conicalP_sph_reg_e(). More...

double	conicalP_sph_reg (int const l, double const lambda, double const x)
	C++ version of gsl_sf_conicalP_sph_reg(). More...

int	conicalP_cyl_reg_e (int const m, double const lambda, double const x, result &result)
	C++ version of gsl_sf_conicalP_cyl_reg_e(). More...

double	conicalP_cyl_reg (int const m, double const lambda, double const x)
	C++ version of gsl_sf_conicalP_cyl_reg(). More...

int	log_e (double const x, result &result)
	C++ version of gsl_sf_log_e(). More...

double	log (double const x)
	C++ version of gsl_sf_log(). More...

int	log_abs_e (double const x, result &result)
	C++ version of gsl_sf_log_abs_e(). More...

double	log_abs (double const x)
	C++ version of gsl_sf_log_abs(). More...

int	complex_log_e (double const zr, double const zi, result &lnr, result &theta)
	C++ version of gsl_sf_complex_log_e(). More...

int	log_1plusx_e (double const x, result &result)
	C++ version of gsl_sf_log_1plusx_e(). More...

double	log_1plusx (double const x)
	C++ version of gsl_sf_log_1plusx(). More...

int	log_1plusx_mx_e (double const x, result &result)
	C++ version of gsl_sf_log_1plusx_mx_e(). More...

double	log_1plusx_mx (double const x)
	C++ version of gsl_sf_log_1plusx_mx(). More...

int	pow_int_e (double x, int n, result &result)
	C++ version of gsl_sf_pow_int_e(). More...

double	pow_int (double const x, int const n)
	C++ version of gsl_sf_pow_int(). More...

int	psi_int_e (int const n, result &result)
	C++ version of gsl_sf_psi_int_e(). More...

double	psi_int (int const n)
	C++ version of gsl_sf_psi_int(). More...

int	psi_e (double const x, result &result)
	C++ version of gsl_sf_psi_e(). More...

double	psi (double const x)
	C++ version of gsl_sf_psi(). More...

int	psi_1piy_e (double const y, result &result)
	C++ version of gsl_sf_psi_1piy_e(). More...

double	psi_1piy (double const y)
	C++ version of gsl_sf_psi_1piy(). More...

int	complex_psi_e (double const x, double const y, result &result_re, result &result_im)
	C++ version of gsl_sf_complex_psi_e(). More...

int	psi_1_int_e (int const n, result &result)
	C++ version of gsl_sf_psi_1_int_e(). More...

double	psi_1_int (int const n)
	C++ version of gsl_sf_psi_1_int(). More...

int	psi_1_e (double const x, result &result)
	C++ version of gsl_sf_psi_1_e(). More...

double	psi_1 (double const x)
	C++ version of gsl_sf_psi_1(). More...

int	psi_n_e (int const n, double const x, result &result)
	C++ version of gsl_sf_psi_n_e(). More...

double	psi_n (int const n, double const x)
	C++ version of gsl_sf_psi_n(). More...

int	result_smash_e (gsl_sf_result_e10 const &re, gsl_sf_result &r)
	C++ version of gsl_sf_result_smash_e(). More...

int	sin_pi_e (double x, result &result)
	C++ version of gsl_sf_sin_pi_e(). More...

double	sin_pi (double const x)
	C++ version of gsl_sf_sin_pi(). More...

int	cos_pi_e (double x, result &result)
	C++ version of gsl_sf_cos_pi_e(). More...

double	cos_pi (double const x)
	C++ version of gsl_sf_cos_pi(). More...

int	synchrotron_1_e (double const x, result &result)
	C++ version of gsl_sf_synchrotron_1_e(). More...

double	synchrotron_1 (double const x)
	C++ version of gsl_sf_synchrotron_1(). More...

int	synchrotron_2_e (double const x, result &result)
	C++ version of gsl_sf_synchrotron_2_e(). More...

double	synchrotron_2 (double const x)
	C++ version of gsl_sf_synchrotron_2(). More...

int	transport_2_e (double const x, result &result)
	C++ version of gsl_sf_transport_2_e(). More...

double	transport_2 (double const x)
	C++ version of gsl_sf_transport_2(). More...

int	transport_3_e (double const x, result &result)
	C++ version of gsl_sf_transport_3_e(). More...

double	transport_3 (double const x)
	C++ version of gsl_sf_transport_3(). More...

int	transport_4_e (double const x, result &result)
	C++ version of gsl_sf_transport_4_e(). More...

double	transport_4 (double const x)
	C++ version of gsl_sf_transport_4(). More...

int	transport_5_e (double const x, result &result)
	C++ version of gsl_sf_transport_5_e(). More...

double	transport_5 (double const x)
	C++ version of gsl_sf_transport_5(). More...

int	sin_e (double x, result &result)
	C++ version of gsl_sf_sin_e(). More...

double	sin (double const x)
	C++ version of gsl_sf_sin(). More...

int	cos_e (double x, result &result)
	C++ version of gsl_sf_cos_e(). More...

double	cos (double const x)
	C++ version of gsl_sf_cos(). More...

int	hypot_e (double const x, double const y, result &result)
	C++ version of gsl_sf_hypot_e(). More...

double	hypot (double const x, double const y)
	C++ version of gsl_sf_hypot(). More...

int	complex_sin_e (double const zr, double const zi, result &szr, result &szi)
	C++ version of gsl_sf_complex_sin_e(). More...

int	complex_cos_e (double const zr, double const zi, result &czr, result &czi)
	C++ version of gsl_sf_complex_cos_e(). More...

int	complex_logsin_e (double const zr, double const zi, result &lszr, result &lszi)
	C++ version of gsl_sf_complex_logsin_e(). More...

int	sinc_e (double x, result &result)
	C++ version of gsl_sf_sinc_e(). More...

double	sinc (double const x)
	C++ version of gsl_sf_sinc(). More...

int	lnsinh_e (double const x, result &result)
	C++ version of gsl_sf_lnsinh_e(). More...

double	lnsinh (double const x)
	C++ version of gsl_sf_lnsinh(). More...

int	lncosh_e (double const x, result &result)
	C++ version of gsl_sf_lncosh_e(). More...

double	lncosh (double const x)
	C++ version of gsl_sf_lncosh(). More...

int	polar_to_rect (double const r, double const theta, result &x, result &y)
	C++ version of gsl_sf_polar_to_rect(). More...

int	rect_to_polar (double const x, double const y, result &r, result &theta)
	C++ version of gsl_sf_rect_to_polar(). More...

int	sin_err_e (double const x, double const dx, result &result)
	C++ version of gsl_sf_sin_err_e(). More...

int	cos_err_e (double const x, double const dx, result &result)
	C++ version of gsl_sf_cos_err_e(). More...

int	angle_restrict_symm_e (double &theta)
	C++ version of gsl_sf_angle_restrict_symm_e(). More...

double	angle_restrict_symm (double const theta)
	C++ version of gsl_sf_angle_restrict_symm(). More...

int	angle_restrict_pos_e (double &theta)
	C++ version of gsl_sf_angle_restrict_pos_e(). More...

double	angle_restrict_pos (double const theta)
	C++ version of gsl_sf_angle_restrict_pos(). More...

int	angle_restrict_symm_err_e (double const theta, result &result)
	C++ version of gsl_sf_angle_restrict_symm_err_e(). More...

int	angle_restrict_pos_err_e (double const theta, result &result)
	C++ version of gsl_sf_angle_restrict_pos_err_e(). More...

int	zeta_int_e (int const n, result &result)
	C++ version of gsl_sf_zeta_int_e(). More...

double	zeta_int (int const n)
	C++ version of gsl_sf_zeta_int(). More...

int	zeta_e (double const s, result &result)
	C++ version of gsl_sf_zeta_e(). More...

double	zeta (double const s)
	C++ version of gsl_sf_zeta(). More...

int	zetam1_e (double const s, result &result)
	C++ version of gsl_sf_zetam1_e(). More...

double	zetam1 (double const s)
	C++ version of gsl_sf_zetam1(). More...

int	zetam1_int_e (int const s, result &result)
	C++ version of gsl_sf_zetam1_int_e(). More...

double	zetam1_int (int const s)
	C++ version of gsl_sf_zetam1_int(). More...

int	hzeta_e (double const s, double const q, result &result)
	C++ version of gsl_sf_hzeta_e(). More...

double	hzeta (double const s, double const q)
	C++ version of gsl_sf_hzeta(). More...

int	eta_int_e (int n, result &result)
	C++ version of gsl_sf_eta_int_e(). More...

double	eta_int (int const n)
	C++ version of gsl_sf_eta_int(). More...

int	eta_e (double const s, result &result)
	C++ version of gsl_sf_eta_e(). More...

double	eta (double const s)
	C++ version of gsl_sf_eta(). More...

Variables
double const	GAMMA_XMAX = GSL_SF_GAMMA_XMAX
	The maximum x such that gamma(x) is not considered an overflow. More...

double const	FACT_NMAX = GSL_SF_FACT_NMAX
	The maximum n such that fact(n) does not give an overflow. More...

double const	DOUBLEFACT_NMAX = GSL_SF_DOUBLEFACT_NMAX
	The maximum n such that doublefact(n) does not give an overflow. More...

Detailed Description

This namespace is used for special functions that in GSL are prefixed gsl_sf.

Note that many of these functions are placed in namespaces within sf. So, for example, gsl_sf_airy_Bi_deriv_e() becomes gsl::sf::airy::deriv_e(). However, other functions such as the trigonometric functions are contained directly in the sf namespace.

Many of the special functions are available in two forms. The first returns an integer indicating any error that occurred and returns the result as a gsl::sf::struct object. The second returns a double. In C++ the second may be preferred because we can use gsl::exception to cause these functions to throw an exception if any problem occurs.

Typedef Documentation

◆ result

typedef gsl_sf_result gsl::sf::result

Typedef for gsl_sf_result.

Definition at line 30 of file sf_result.hpp.

◆ result_e10

typedef gsl_sf_result_e10 gsl::sf::result_e10

Typedef for gsl_sf_result_e10.

Definition at line 34 of file sf_result.hpp.

Function Documentation

◆ angle_restrict_pos()

double gsl::sf::angle_restrict_pos ( double const theta )

inline

C++ version of gsl_sf_angle_restrict_pos().

Force an angle to lie in the range [0, 2pi)

Parameters

theta A real value (angle)

Returns: The function value

Definition at line 236 of file sf_trig.hpp.

◆ angle_restrict_pos_e()

int gsl::sf::angle_restrict_pos_e ( double & theta )

inline

C++ version of gsl_sf_angle_restrict_pos_e().

Force an angle to lie in the range [0, 2pi)

Parameters

theta A real value (angle)

Returns: GSL_SUCCESS or GSL_ELOSS

Definition at line 228 of file sf_trig.hpp.

◆ angle_restrict_pos_err_e()

int gsl::sf::angle_restrict_pos_err_e	(	double const	theta,
		result &	result
	)

inline

C++ version of gsl_sf_angle_restrict_pos_err_e().

Parameters

theta	A real value (angle)
result	The result as a `gsl::sf::result` object

Returns: Error code on failure

Definition at line 252 of file sf_trig.hpp.

◆ angle_restrict_symm()

double gsl::sf::angle_restrict_symm ( double const theta )

inline

C++ version of gsl_sf_angle_restrict_symm().

Force an angle to lie in the range (-pi,pi].

Parameters

theta A real value (angle)

Returns: The function value

Definition at line 210 of file sf_trig.hpp.

◆ angle_restrict_symm_e()

int gsl::sf::angle_restrict_symm_e ( double & theta )

inline

C++ version of gsl_sf_angle_restrict_symm_e().

Force an angle to lie in the range (-pi,pi].

Parameters

theta A real value (angle)

Returns: GSL_SUCCESS or GSL_ELOSS

Definition at line 202 of file sf_trig.hpp.

◆ angle_restrict_symm_err_e()

int gsl::sf::angle_restrict_symm_err_e	(	double const	theta,
		result &	result
	)

inline

C++ version of gsl_sf_angle_restrict_symm_err_e().

Parameters

theta	A real value (angle)
result	The result as a `gsl::sf::result` object

Returns: Error code on failure

Definition at line 244 of file sf_trig.hpp.

◆ atanint()

double gsl::sf::atanint ( double const x )

inline

C++ version of gsl_sf_atanint().

AtanInt(x) := Integral[ Arctan[t]/t, {t,0,x}]

Parameters

x	A real number

Returns: The function value

Definition at line 296 of file sf_expint.hpp.

◆ atanint_e()

int gsl::sf::atanint_e	(	double const	x,
		result &	result
	)

inline

C++ version of gsl_sf_atanint_e().

AtanInt(x) := Integral[ Arctan[t]/t, {t,0,x}]

Parameters

x	A real number
result	The result as a `gsl::sf::result` object

Returns: Error code on failure

Definition at line 289 of file sf_expint.hpp.

◆ beta()

double gsl::sf::beta	(	double const	a,
		double const	b
	)

inline

C++ version of gsl_sf_beta().

Beta Function B(a,b)

a > 0, b > 0

Parameters

a	A real number
b	A real number

Returns: The function value

Definition at line 552 of file sf_gamma.hpp.

References gsl::sf::mathieu::a(), and gsl::sf::mathieu::b().

◆ beta_e()

int gsl::sf::beta_e	(	double const	a,
		double const	b,
		result &	result
	)

inline

C++ version of gsl_sf_beta_e().

Beta Function B(a,b)

a > 0, b > 0

Parameters

a	A real number
b	A real number
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS or GSL_EOVRFLW or GSL_EUNDRFLW or GSL_EDOM

Definition at line 540 of file sf_gamma.hpp.

References gsl::sf::mathieu::a(), and gsl::sf::mathieu::b().

◆ beta_inc()

double gsl::sf::beta_inc	(	double const	a,
		double const	b,
		double const	x
	)

inline

C++ version of gsl_sf_beta_inc().

Normalized Incomplete Beta Function B_x(a,b)/B(a,b)

a > 0, b > 0, 0 <= x <= 1

Parameters

a	A real number
b	A real number
x	A real number

Returns: The function value

Definition at line 578 of file sf_gamma.hpp.

References gsl::sf::mathieu::a(), and gsl::sf::mathieu::b().

◆ beta_inc_e()

int gsl::sf::beta_inc_e	(	double const	a,
		double const	b,
		double const	x,
		result &	result
	)

inline

C++ version of gsl_sf_beta_inc_e().

Normalized Incomplete Beta Function B_x(a,b)/B(a,b)

a > 0, b > 0, 0 <= x <= 1

Parameters

a	A real number
b	A real number
x	A real number
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS or GSL_EDOM or GSL_EUNDRFLW

Definition at line 565 of file sf_gamma.hpp.

References gsl::sf::mathieu::a(), and gsl::sf::mathieu::b().

◆ Chi()

double gsl::sf::Chi ( double const x )

inline

C++ version of gsl_sf_Chi().

Chi(x) := Re[ M_EULER + log(x) + Integrate[(Cosh[t]-1)/t, {t,0,x}] ]

x != 0.0

Parameters

x	A real number

Returns: The function value

Definition at line 228 of file sf_expint.hpp.

◆ Chi_e()

int gsl::sf::Chi_e	(	double const	x,
		result &	result
	)

inline

C++ version of gsl_sf_Chi_e().

Chi(x) := Re[ M_EULER + log(x) + Integrate[(Cosh[t]-1)/t, {t,0,x}] ]

x != 0.0

Parameters

x	A real number
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS or GSL_EDOM or GSL_EOVRFLW or GSL_EUNDRFLW

Definition at line 219 of file sf_expint.hpp.

◆ choose()

double gsl::sf::choose	(	unsigned int	n,
		unsigned int	m
	)

inline

C++ version of gsl_sf_choose().

n choose m

Parameters

n	An integer
m	An integer

Returns: The function value

Definition at line 279 of file sf_gamma.hpp.

References gsl::rstat::n().

◆ choose_e()

int gsl::sf::choose_e	(	unsigned int	n,
		unsigned int	m,
		result &	result
	)

inline

C++ version of gsl_sf_choose_e().

n choose m

Parameters

n	An integer
m	An integer
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS or GSL_EDOM or GSL_EOVRFLW

Definition at line 270 of file sf_gamma.hpp.

References gsl::rstat::n().

◆ Ci()

double gsl::sf::Ci ( double const x )

inline

C++ version of gsl_sf_Ci().

Ci(x) := -Integrate[ Cos[t]/t, {t,x,Infinity}]

x > 0.0

Parameters

x	A real number

Returns: The function value

Definition at line 281 of file sf_expint.hpp.

◆ Ci_e()

int gsl::sf::Ci_e	(	double const	x,
		result &	result
	)

inline

C++ version of gsl_sf_Ci_e().

Ci(x) := -Integrate[ Cos[t]/t, {t,x,Infinity}]

x > 0.0

Parameters

x	A real number
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS or GSL_EDOM

Definition at line 272 of file sf_expint.hpp.

◆ clausen()

double gsl::sf::clausen ( double const x )

inline

C++ version of gsl_sf_clausen().

Calculate the Clausen integral: Cl_2(x) := Integrate[-Log[2 Sin[t/2]], {t,0,x}]

Relation to dilogarithm: Cl_2(theta) = Im[ Li_2(e^(i theta)) ]

Parameters

x	A real value

Returns: The function applied to x

Definition at line 52 of file sf_clausen.hpp.

◆ clausen_e()

int gsl::sf::clausen_e	(	double const	x,
		result &	result
	)

inline

C++ version of gsl_sf_clausen().

Calculate the Clausen integral: Cl_2(x) := Integrate[-Log[2 Sin[t/2]], {t,0,x}]

Relation to dilogarithm: Cl_2(theta) = Im[ Li_2(e^(i theta)) ]

Parameters

x	A real value
result	The result as a `gsl::sf::result` object

Returns: Error code on failure

Definition at line 40 of file sf_clausen.hpp.

◆ complex_cos_e()

int gsl::sf::complex_cos_e	(	double const	zr,
		double const	zi,
		result &	czr,
		result &	czi
	)

inline

C++ version of gsl_sf_complex_cos_e().

Parameters

zr	Real part of a complex number
zi	Imaginary part of a complex number
czr	The real part of the result as a `gsl::sf::result` object
czi	The imaginary part of the result as a `gsl::sf::result` object

Returns: GSL_SUCCESS or GSL_EOVRFLW

Definition at line 89 of file sf_trig.hpp.

◆ complex_dilog_e()

int gsl::sf::complex_dilog_e	(	double const	r,
		double const	theta,
		result &	result_re,
		result &	result_im
	)

inline

C++ version of gsl_sf_complex_dilog_e().

DiLogarithm(z), for complex argument z = r Exp[i theta]. Computes the principal branch, thereby assuming an implicit reduction of theta to the range (-2 pi, 2 pi).

Parameters

r	A real number
theta	A real number
result_re	Real part of result as `gsl::sf::result` object
result_im	Imaginary part of result as `gsl::sf::result` object

Returns: Error code on failure

Definition at line 73 of file sf_dilog.hpp.

◆ complex_dilog_xy_e()

int gsl::sf::complex_dilog_xy_e	(	double const	x,
		double const	y,
		result &	result_re,
		result &	result_im
	)

inline

C++ version of gsl_sf_complex_dilog_xy_e().

DiLogarithm(z), for complex argument z = x + i y. Computes the principal branch.

Parameters

x	A real number
y	A real number
result_re	Real part of result as `gsl::sf::result` object
result_im	Imaginary part of result as `gsl::sf::result` object

Returns: Error code on failure

Definition at line 60 of file sf_dilog.hpp.

◆ complex_log_e()

int gsl::sf::complex_log_e	(	double const	zr,
		double const	zi,
		result &	lnr,
		result &	theta
	)

inline

C++ version of gsl_sf_complex_log_e().

Complex Logarithm exp(lnr + I theta) = zr + I zi Returns argument in [-pi,pi].

Parameters

zr	Real part of a complex number
zi	Imaginary part of a complex number
lnr	The result (ln r) as a gsl::sf::result object
theta	The result (theta) as a gsl::sf::result object

Returns: GSL_SUCCESS or GSL_EDOM

Definition at line 69 of file sf_log.hpp.

◆ complex_logsin_e()

int gsl::sf::complex_logsin_e	(	double const	zr,
		double const	zi,
		result &	lszr,
		result &	lszi
	)

inline

C++ version of gsl_sf_complex_logsin_e().

Parameters

zr	Real part of a complex number
zi	Imaginary part of a complex number
lszr	The real part of the result as a `gsl::sf::result` object
lszi	The imaginary part of the result as a `gsl::sf::result` object

Returns: GSL_SUCCESS or GSL_EDOM or GSL_ELOSS

Definition at line 99 of file sf_trig.hpp.

◆ complex_psi_e()

int gsl::sf::complex_psi_e	(	double const	x,
		double const	y,
		result &	result_re,
		result &	result_im
	)

inline

C++ version of gsl_sf_complex_psi_e().

Poly-Gamma Functions

psi(m,x) := (d/dx)^m psi(0,x) = (d/dx)^{m+1} log(gamma(x))

Parameters

x	Real part of complex number
y	Imaginary part of complex number
result_re	Real part of result as `gsl::sf::result` object
result_im	Imaginary part of result as `gsl::sf::result` object

Returns: GSL_SUCCESS

Definition at line 117 of file sf_psi.hpp.

◆ complex_sin_e()

int gsl::sf::complex_sin_e	(	double const	zr,
		double const	zi,
		result &	szr,
		result &	szi
	)

inline

C++ version of gsl_sf_complex_sin_e().

Parameters

zr	Real part of a complex number
zi	Imaginary part of a complex number
szr	The real part of the result as a `gsl::sf::result` object
szi	The imaginary part of the result as a `gsl::sf::result` object

Returns: GSL_SUCCESS or GSL_EOVRFLW

Definition at line 79 of file sf_trig.hpp.

◆ complex_spence_xy_e()

int gsl::sf::complex_spence_xy_e	(	double const	x,
		double const	y,
		result &	real_sp,
		result &	imag_sp
	)

inline

C++ version of gsl_sf_complex_spence_xy_e().

Spence integral; spence(s) := Li_2(1-s)

Parameters

x	A real number
y	A real number
real_sp	Real part of result as `gsl::sf::result` object
imag_sp	Imaginary part of result as `gsl::sf::result` object

Returns: Error code on failure

Definition at line 84 of file sf_dilog.hpp.

◆ conicalP_0()

double gsl::sf::conicalP_0	(	double const	lambda,
		double const	x
	)

inline

C++ version of gsl_sf_conicalP_0().

Conical Function P^{0}_{-1/2 + I lambda}(x)

x > -1.0

Parameters

lambda	A real value
x	A real value

Returns: The function value

Definition at line 491 of file sf_legendre.hpp.

◆ conicalP_0_e()

int gsl::sf::conicalP_0_e	(	double const	lambda,
		double const	x,
		result &	result
	)

inline

C++ version of gsl_sf_conicalP_0_e().

Conical Function P^{0}_{-1/2 + I lambda}(x)

x > -1.0

Parameters

lambda	A real value
x	A real value
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS or GSL_EDOM

Definition at line 479 of file sf_legendre.hpp.

◆ conicalP_1()

double gsl::sf::conicalP_1	(	double const	lambda,
		double const	x
	)

inline

C++ version of gsl_sf_conicalP_1().

Conical Function P^{1}_{-1/2 + I lambda}(x)

x > -1.0

Parameters

lambda	A real value
x	A real value

Returns: The function value

Definition at line 516 of file sf_legendre.hpp.

◆ conicalP_1_e()

int gsl::sf::conicalP_1_e	(	double const	lambda,
		double const	x,
		result &	result
	)

inline

C++ version of gsl_sf_conicalP_1_e().

Conical Function P^{1}_{-1/2 + I lambda}(x)

x > -1.0

Parameters

lambda	A real value
x	A real value
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS or GSL_EDOM

Definition at line 504 of file sf_legendre.hpp.

◆ conicalP_cyl_reg()

double gsl::sf::conicalP_cyl_reg	(	int const	m,
		double const	lambda,
		double const	x
	)

inline

C++ version of gsl_sf_conicalP_cyl_reg().

Regular Cylindrical Conical Function P^{-m}_{-1/2 + I lambda}(x)

x > -1.0, m >= -1

Parameters

m	An integer
lambda	A real value
x	A real value

Returns: The function value

Definition at line 570 of file sf_legendre.hpp.

◆ conicalP_cyl_reg_e()

int gsl::sf::conicalP_cyl_reg_e	(	int const	m,
		double const	lambda,
		double const	x,
		result &	result
	)

inline

C++ version of gsl_sf_conicalP_cyl_reg_e().

Regular Cylindrical Conical Function P^{-m}_{-1/2 + I lambda}(x)

x > -1.0, m >= -1

Parameters

m	An integer
lambda	A real value
x	A real value
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS or GSL_EDOM

Definition at line 557 of file sf_legendre.hpp.

◆ conicalP_half()

double gsl::sf::conicalP_half	(	double const	lambda,
		double const	x
	)

inline

C++ version of gsl_sf_conicalP_half().

Irregular Spherical Conical Function P^{1/2}_{-1/2 + I lambda}(x)

x > -1.0

Parameters

lambda	A real value
x	A real value

Returns: The function value

Definition at line 441 of file sf_legendre.hpp.

◆ conicalP_half_e()

int gsl::sf::conicalP_half_e	(	double const	lambda,
		double const	x,
		result &	result
	)

inline

Definition at line 429 of file sf_legendre.hpp.

◆ conicalP_mhalf()

double gsl::sf::conicalP_mhalf	(	double const	lambda,
		double const	x
	)

inline

C++ version of gsl_sf_conicalP_mhalf().

Regular Spherical Conical Function P^{-1/2}_{-1/2 + I lambda}(x)

x > -1.0

Parameters

lambda	A real value
x	A real value

Returns: The function value

Definition at line 466 of file sf_legendre.hpp.

◆ conicalP_mhalf_e()

int gsl::sf::conicalP_mhalf_e	(	double const	lambda,
		double const	x,
		result &	result
	)

inline

C++ version of gsl_sf_conicalP_mhalf_e().

Regular Spherical Conical Function P^{-1/2}_{-1/2 + I lambda}(x)

x > -1.0

Parameters

lambda	A real value
x	A real value
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS or GSL_EDOM

Definition at line 454 of file sf_legendre.hpp.

◆ conicalP_sph_reg()

double gsl::sf::conicalP_sph_reg	(	int const	l,
		double const	lambda,
		double const	x
	)

inline

C++ version of gsl_sf_conicalP_sph_reg().

Regular Spherical Conical Function P^{-1/2-l}_{-1/2 + I lambda}(x)

x > -1.0, l >= -1

Parameters

l	An integer
lambda	A real value
x	A real value

Returns: The function value

Definition at line 543 of file sf_legendre.hpp.

◆ conicalP_sph_reg_e()

int gsl::sf::conicalP_sph_reg_e	(	int const	l,
		double const	lambda,
		double const	x,
		result &	result
	)

inline

C++ version of gsl_sf_conicalP_sph_reg_e().

Regular Spherical Conical Function P^{-1/2-l}_{-1/2 + I lambda}(x)

x > -1.0, l >= -1

Parameters

l	An integer
lambda	A real value
x	A real value
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS or GSL_EDOM

Definition at line 530 of file sf_legendre.hpp.

◆ cos()

double gsl::sf::cos ( double const x )

inline

C++ version of gsl_sf_cos().

Parameters

x	A real value

Returns: The function value

Definition at line 54 of file sf_trig.hpp.

◆ cos_e()

int gsl::sf::cos_e	(	double	x,
		result &	result
	)

inline

C++ version of gsl_sf_cos_e().

Parameters

x	A real value
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS

Definition at line 48 of file sf_trig.hpp.

◆ cos_err_e()

int gsl::sf::cos_err_e	(	double const	x,
		double const	dx,
		result &	result
	)

inline

C++ version of gsl_sf_cos_err_e().

Cos(x) for quantity with an associated error.

Parameters

x	A real value
dx	The error in `x`
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS

Definition at line 184 of file sf_trig.hpp.

◆ cos_pi()

double gsl::sf::cos_pi ( double const x )

inline

C++ version of gsl_sf_cos_pi().

Cosine function

Parameters

x	A real number

Returns: The function value

Definition at line 58 of file sf_sincos_pi.hpp.

◆ cos_pi_e()

int gsl::sf::cos_pi_e	(	double	x,
		result &	result
	)

inline

C++ version of gsl_sf_cos_pi_e().

Cosine function

Parameters

x	A real number
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS or GSL_EOVRFLW or GSL_EUNDRFLW

Definition at line 51 of file sf_sincos_pi.hpp.

◆ coupling_3j()

double gsl::sf::coupling_3j	(	int	two_ja,
		int	two_jb,
		int	two_jc,
		int	two_ma,
		int	two_mb,
		int	two_mc
	)

inline

C++ version of gsl_sf_coupling_3j().

Parameters

two_ja	Coupling coefficient in half-integer units
two_jb	Coupling coefficient in half-integer units
two_jc	Coupling coefficient in half-integer units
two_ma	Coupling coefficient in half-integer units
two_mb	Coupling coefficient in half-integer units
two_mc	Coupling coefficient in half-integer units

Returns: The Wigner 3-j coefficient

Definition at line 53 of file sf_coupling.hpp.

◆ coupling_3j_e()

int gsl::sf::coupling_3j_e	(	int	two_ja,
		int	two_jb,
		int	two_jc,
		int	two_ma,
		int	two_mb,
		int	two_mc,
		result &	result
	)

inline

C++ version of gsl_sf_coupling_3j().

Parameters

two_ja	Coupling coefficient in half-integer units
two_jb	Coupling coefficient in half-integer units
two_jc	Coupling coefficient in half-integer units
two_ma	Coupling coefficient in half-integer units
two_mb	Coupling coefficient in half-integer units
two_mc	Coupling coefficient in half-integer units
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS or GSL_EDOM or GSL_EOVERFLW

Definition at line 40 of file sf_coupling.hpp.

◆ coupling_6j()

double gsl::sf::coupling_6j	(	int	two_ja,
		int	two_jb,
		int	two_jc,
		int	two_jd,
		int	two_je,
		int	two_jf
	)

inline

C++ version of gsl_sf_coupling_6j().

Parameters

two_ja	Coupling coefficient in half-integer units
two_jb	Coupling coefficient in half-integer units
two_jc	Coupling coefficient in half-integer units
two_jd	Coupling coefficient in half-integer units
two_je	Coupling coefficient in half-integer units
two_jf	Coupling coefficient in half-integer units

Returns: The Wigner 6-j coefficient

Definition at line 79 of file sf_coupling.hpp.

◆ coupling_6j_e()

int gsl::sf::coupling_6j_e	(	int	two_ja,
		int	two_jb,
		int	two_jc,
		int	two_jd,
		int	two_je,
		int	two_jf,
		result &	result
	)

inline

C++ version of gsl_sf_coupling_6j_e().

Parameters

two_ja	Coupling coefficient in half-integer units
two_jb	Coupling coefficient in half-integer units
two_jc	Coupling coefficient in half-integer units
two_jd	Coupling coefficient in half-integer units
two_je	Coupling coefficient in half-integer units
two_jf	Coupling coefficient in half-integer units
result	Coupling coefficient in half-integer units

Returns: GSL_SUCCESS or GSL_EDOM or GSL_EOVERFLW

Definition at line 66 of file sf_coupling.hpp.

◆ coupling_9j()

double gsl::sf::coupling_9j	(	int	two_ja,
		int	two_jb,
		int	two_jc,
		int	two_jd,
		int	two_je,
		int	two_jf,
		int	two_jg,
		int	two_jh,
		int	two_ji
	)

inline

C++ version of gsl_sf_coupling_9j().

Parameters

two_ja	Coupling coefficient in half-integer units
two_jb	Coupling coefficient in half-integer units
two_jc	Coupling coefficient in half-integer units
two_jd	Coupling coefficient in half-integer units
two_je	Coupling coefficient in half-integer units
two_jf	Coupling coefficient in half-integer units
two_jg	Coupling coefficient in half-integer units
two_jh	Coupling coefficient in half-integer units
two_ji	Coupling coefficient in half-integer units

Returns: The Wigner 9-j coefficient

Definition at line 138 of file sf_coupling.hpp.

◆ coupling_9j_e()

int gsl::sf::coupling_9j_e	(	int	two_ja,
		int	two_jb,
		int	two_jc,
		int	two_jd,
		int	two_je,
		int	two_jf,
		int	two_jg,
		int	two_jh,
		int	two_ji,
		result &	result
	)

inline

C++ version of gsl_sf_coupling_9j_e().

Parameters

two_ja	Coupling coefficient in half-integer units
two_jb	Coupling coefficient in half-integer units
two_jc	Coupling coefficient in half-integer units
two_jd	Coupling coefficient in half-integer units
two_je	Coupling coefficient in half-integer units
two_jf	Coupling coefficient in half-integer units
two_jg	Coupling coefficient in half-integer units
two_jh	Coupling coefficient in half-integer units
two_ji	Coupling coefficient in half-integer units
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS or GSL_EDOM or GSL_EOVERFLW

Definition at line 121 of file sf_coupling.hpp.

◆ coupling_RacahW()

double gsl::sf::coupling_RacahW	(	int	two_ja,
		int	two_jb,
		int	two_jc,
		int	two_jd,
		int	two_je,
		int	two_jf
	)

inline

C++ version of gsl_sf_coupling_RacahW().

Parameters

two_ja	Coupling coefficient in half-integer units
two_jb	Coupling coefficient in half-integer units
two_jc	Coupling coefficient in half-integer units
two_jd	Coupling coefficient in half-integer units
two_je	Coupling coefficient in half-integer units
two_jf	Coupling coefficient in half-integer units

Returns: The function value

Definition at line 105 of file sf_coupling.hpp.

◆ coupling_RacahW_e()

int gsl::sf::coupling_RacahW_e	(	int	two_ja,
		int	two_jb,
		int	two_jc,
		int	two_jd,
		int	two_je,
		int	two_jf,
		result &	result
	)

inline

C++ version of gsl_sf_coupling_RacahW_e().

Parameters

two_ja	Coupling coefficient in half-integer units
two_jb	Coupling coefficient in half-integer units
two_jc	Coupling coefficient in half-integer units
two_jd	Coupling coefficient in half-integer units
two_je	Coupling coefficient in half-integer units
two_jf	Coupling coefficient in half-integer units
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS or GSL_EDOM or GSL_EOVERFLW

Definition at line 92 of file sf_coupling.hpp.

◆ dawson()

double gsl::sf::dawson ( double x )

inline

C++ version of gsl_sf_dawson().

Dawson's integral:

Exp[-x^2] Integral[ Exp[t^2], {t,0,x}]

Parameters

x	A real number

Returns: The integral

Definition at line 47 of file sf_dawson.hpp.

◆ dawson_e()

int gsl::sf::dawson_e	(	double	x,
		result &	result
	)

inline

C++ version of gsl_sf_dawson_e().

Dawson's integral:

Exp[-x^2] Integral[ Exp[t^2], {t,0,x}]

Parameters

x	A real number
result	The result as a `gsl::sf::result` object

Returns: Error code on failure

Definition at line 38 of file sf_dawson.hpp.

◆ debye_1()

double gsl::sf::debye_1 ( double const x )

inline

C++ version of gsl_sf_debye_1().

D_1(x) := n/x^n Integrate[t^1/(e^t - 1), {t,0,x}]

Parameters

x	A real number

Returns: The function value

Definition at line 43 of file sf_debye.hpp.

◆ debye_1_e()

int gsl::sf::debye_1_e	(	double const	x,
		result &	result
	)

inline

C++ version of gsl_sf_debye_1_e().

D_1(x) := 1/x Integrate[t/(e^t - 1), {t,0,x}]

Parameters

x	A real number
result	The result as a `gsl::sf::result` object

Returns: Error code on failure

Definition at line 36 of file sf_debye.hpp.

◆ debye_2()

double gsl::sf::debye_2 ( double const x )

inline

C++ version of gsl_sf_debye_2().

D_2(x) := 2/x^2 Integrate[t^2/(e^t - 1), {t,0,x}]

Parameters

x	A real number

Returns: The function value

Definition at line 58 of file sf_debye.hpp.

◆ debye_2_e()

int gsl::sf::debye_2_e	(	double const	x,
		result &	result
	)

inline

C++ version of gsl_sf_debye_2_e().

D_2(x) := 2/x^2 Integrate[t^2/(e^t - 1), {t,0,x}]

Parameters

x	A real number
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS or GSL_EDOM

Definition at line 51 of file sf_debye.hpp.

◆ debye_3()

double gsl::sf::debye_3 ( double const x )

inline

C++ version of gsl_sf_debye_3().

D_3(x) := 3/x^3 Integrate[t^3/(e^t - 1), {t,0,x}]

Parameters

x	A real number

Returns: The function value

Definition at line 73 of file sf_debye.hpp.

◆ debye_3_e()

int gsl::sf::debye_3_e	(	double const	x,
		result &	result
	)

inline

C++ version of gsl_sf_debye_3_e().

D_3(x) := 3/x^3 Integrate[t^3/(e^t - 1), {t,0,x}]

Parameters

x	A real number
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS or GSL_EDOM or GSL_UNDRFLW

Definition at line 66 of file sf_debye.hpp.

◆ debye_4()

double gsl::sf::debye_4 ( double const x )

inline

C++ version of gsl_sf_debye_4().

D_4(x) := 4/x^4 Integrate[t^4/(e^t - 1), {t,0,x}]

Parameters

x	A real number

Returns: The function value

Definition at line 88 of file sf_debye.hpp.

◆ debye_4_e()

int gsl::sf::debye_4_e	(	double const	x,
		result &	result
	)

inline

C++ version of gsl_sf_debye_4_e().

D_4(x) := 4/x^4 Integrate[t^4/(e^t - 1), {t,0,x}]

Parameters

x	A real number
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS or GSL_EDOM or GSL_UNDRFLW

Definition at line 81 of file sf_debye.hpp.

◆ debye_5()

double gsl::sf::debye_5 ( double const x )

inline

C++ version of gsl_sf_debye_5().

D_5(x) := 5/x^5 Integrate[t^5/(e^t - 1), {t,0,x}]

Parameters

x	A real number

Returns: The function value

Definition at line 103 of file sf_debye.hpp.

◆ debye_5_e()

int gsl::sf::debye_5_e	(	double const	x,
		result &	result
	)

inline

C++ version of gsl_sf_debye_5_e().

D_5(x) := 5/x^5 Integrate[t^5/(e^t - 1), {t,0,x}]

Parameters

x	A real number
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS or GSL_EDOM or GSL_UNDRFLW

Definition at line 96 of file sf_debye.hpp.

◆ debye_6()

double gsl::sf::debye_6 ( double const x )

inline

C++ version of gsl_sf_debye_6().

D_6(x) := 6/x^6 Integrate[t^6/(e^t - 1), {t,0,x}]

Parameters

x	A real number

Returns: The function value

Definition at line 118 of file sf_debye.hpp.

◆ debye_6_e()

int gsl::sf::debye_6_e	(	double const	x,
		result &	result
	)

inline

C++ version of gsl_sf_debye_6_e().

D_6(x) := 6/x^6 Integrate[t^6/(e^t - 1), {t,0,x}]

Parameters

x	A real number
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS or GSL_EDOM or GSL_UNDRFLW

Definition at line 111 of file sf_debye.hpp.

◆ dilog()

double gsl::sf::dilog ( double const x )

inline

C++ version of gsl_sf_dilog().

Real part of DiLogarithm(x), for real argument. In Lewin's notation, this is Li_2(x).

Li_2(x) = - Re[ Integrate[ Log[1-s] / s, {s, 0, x}] ]

Parameters

x	A real number

Returns: Error code on failure

Definition at line 49 of file sf_dilog.hpp.

◆ dilog_e()

int gsl::sf::dilog_e	(	double	x,
		result &	result
	)

inline

C++ version of gsl_sf_dilog().

Real part of DiLogarithm(x), for real argument. In Lewin's notation, this is Li_2(x).

Li_2(x) = - Re[ Integrate[ Log[1-s] / s, {s, 0, x}] ]

Parameters

x	A real number
result	The result as a `gsl::sf::result` object

Returns: Error code on failure

Definition at line 39 of file sf_dilog.hpp.

◆ doublefact()

double gsl::sf::doublefact ( unsigned int const n )

inline

C++ version of gsl_sf_doublefact().

n!! = n(n-2)(n-4) ...

Parameters

n	An integer

Returns: The function value

Definition at line 207 of file sf_gamma.hpp.

References gsl::rstat::n().

◆ doublefact_e()

int gsl::sf::doublefact_e	(	unsigned int const	n,
		result &	result
	)

inline

C++ version of gsl_sf_doublefact_e().

n!! = n(n-2)(n-4) ...

Parameters

n	An integer
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS or GSL_EDOM or GSL_EOVRFLW

Definition at line 199 of file sf_gamma.hpp.

References gsl::rstat::n().

◆ elljac_e()

int gsl::sf::elljac_e	(	double const	u,
		double const	m,
		double &	sn,
		double &	cn,
		double &	dn
	)

inline

C++ version of gsl_sf_elljac_e().

Jacobian elliptic functions sn, dn, cn, by descending Landen transformations

Parameters

u	A real number
m	A real number
sn	A real number
cn	A real number
dn	A real number

Returns: GSL_SUCCESS or GSL_EDOM

Definition at line 55 of file sf_elljac.hpp.

◆ erf()

double gsl::sf::erf ( double x )

inline

C++ version of gsl_sf_erf().

Error Function erf(x) := 2/Sqrt[Pi] Integrate[Exp[-t^2], {t,0,x}]

Parameters

x	A real number

Returns: The function value

Definition at line 77 of file sf_erf.hpp.

◆ erf_e()

int gsl::sf::erf_e	(	double	x,
		result &	result
	)

inline

C++ version of gsl_sf_erf_e().

Error Function erf(x) := 2/Sqrt[Pi] Integrate[Exp[-t^2], {t,0,x}]

Parameters

x	A real number
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS

Definition at line 69 of file sf_erf.hpp.

◆ erf_Q()

double gsl::sf::erf_Q ( double x )

inline

C++ version of gsl_sf_erf_Q().

Probability function Q(x) : Abramowitz+Stegun 26.2.3

Parameters

x	A real number

Returns: The function value

Definition at line 111 of file sf_erf.hpp.

◆ erf_Q_e()

int gsl::sf::erf_Q_e	(	double	x,
		result &	result
	)

inline

C++ version of gsl_sf_erf_Q_e().

Probability function Q(x) : Abramowitz+Stegun 26.2.3

Parameters

x	A real number
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS

Definition at line 95 of file sf_erf.hpp.

◆ erf_Z()

double gsl::sf::erf_Z ( double x )

inline

C++ version of gsl_sf_erf_Z().

Probability function Z(x) : Abramowitz+Stegun 26.2.1

Parameters

x	A real number

Returns: The function value

Definition at line 103 of file sf_erf.hpp.

◆ erf_Z_e()

int gsl::sf::erf_Z_e	(	double	x,
		result &	result
	)

inline

C++ version of gsl_sf_erf_Z_e().

Probability function Z(x) : Abramowitz+Stegun 26.2.1

Parameters

x	A real number
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS

Definition at line 86 of file sf_erf.hpp.

◆ erfc()

double gsl::sf::erfc ( double x )

inline

C++ version of gsl_sf_erfc().

Complementary Error Function erfc(x) := 2/Sqrt[Pi] Integrate[Exp[-t^2], {t,x,Infinity}]

Parameters

x	A real number

Returns: The function value

Definition at line 45 of file sf_erf.hpp.

◆ erfc_e()

int gsl::sf::erfc_e	(	double	x,
		result &	result
	)

inline

C++ version of gsl_sf_erfc_e().

Complementary Error Function erfc(x) := 2/Sqrt[Pi] Integrate[Exp[-t^2], {t,x,Infinity}]

Parameters

x	A real number
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS

Definition at line 37 of file sf_erf.hpp.

◆ eta()

double gsl::sf::eta ( double const s )

inline

C++ version of gsl_sf_eta().

Eta Function eta(s) = (1-2^(1-s)) zeta(s)

Parameters

s	A real value

Returns: The function value

Definition at line 181 of file sf_zeta.hpp.

Referenced by gsl::sf::coulomb::CL_array(), gsl::sf::coulomb::CL_e(), gsl::sf::legendre::H3d(), gsl::sf::legendre::H3d_0(), gsl::sf::legendre::H3d_0_e(), gsl::sf::legendre::H3d_1(), gsl::sf::legendre::H3d_1_e(), gsl::sf::legendre::H3d_array(), gsl::sf::legendre::H3d_e(), gsl::multilarge::linear::lcurve(), gsl::multifit::linear_lcorner(), gsl::multifit::linear_lcorner2(), gsl::multifit::linear_lcurvature(), gsl::multifit::linear_lcurve(), gsl::sf::coulomb::wave_F_array(), gsl::sf::coulomb::wave_FG_array(), gsl::sf::coulomb::wave_FG_e(), gsl::sf::coulomb::wave_FGp_array(), and gsl::sf::coulomb::wave_sphF_array().

◆ eta_e()

int gsl::sf::eta_e	(	double const	s,
		result &	result
	)

inline

C++ version of gsl_sf_eta_e().

Eta Function eta(s) = (1-2^(1-s)) zeta(s)

Parameters

s	A real value
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS or GSL_EUNDRFLW or GSL_EOVRFLW

Definition at line 172 of file sf_zeta.hpp.

◆ eta_int()

double gsl::sf::eta_int ( int const n )

inline

C++ version of gsl_sf_eta_int().

Eta Function eta(n) = (1-2^(1-n)) zeta(n)

Parameters

n	An integer

Returns: The function value

Definition at line 163 of file sf_zeta.hpp.

References gsl::rstat::n().

◆ eta_int_e()

int gsl::sf::eta_int_e	(	int	n,
		result &	result
	)

inline

C++ version of gsl_sf_eta_int_e().

Eta Function eta(n) = (1-2^(1-n)) zeta(n)

Parameters

n	An integer
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS or GSL_EUNDRFLW or GSL_EOVRFLW

Definition at line 154 of file sf_zeta.hpp.

References gsl::rstat::n().

◆ exp()

double gsl::sf::exp ( double const x )

inline

C++ version of gsl_sf_exp().

Exponential function

Parameters

x	A real number

Returns: The function value

Definition at line 43 of file sf_exp.hpp.

◆ exp_e()

int gsl::sf::exp_e	(	double	x,
		result &	result
	)

inline

C++ version of gsl_sf_exp_e().

Exponential function

Parameters

x	A real number
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS or GSL_EOVRFLW or GSL_EUNDRFLW

Definition at line 36 of file sf_exp.hpp.

◆ exp_e10_e()

int gsl::sf::exp_e10_e	(	double const	x,
		result_e10 &	result
	)

inline

C++ version of gsl_sf_exp_e10_e().

Exp(x)

Parameters

x	A real number
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS or GSL_EUNDRFLW or GSL_EOVRFLW

Definition at line 51 of file sf_exp.hpp.

◆ exp_err_e()

int gsl::sf::exp_err_e	(	double const	x,
		double const	dx,
		result &	result
	)

inline

C++ version of gsl_sf_exp_err_e().

Exponentiate a quantity with an associated error.

Parameters

x	A real number
dx	A real number
result	The result as a `gsl::sf::result` object

Returns: Error code on failure

Definition at line 176 of file sf_exp.hpp.

◆ exp_err_e10_e()

int gsl::sf::exp_err_e10_e	(	double const	x,
		double const	dx,
		result_e10 &	result
	)

inline

C++ version of gsl_sf_exp_err_e10_e().

Exponentiate a quantity with an associated error.

Parameters

x	A real number
dx	A real number
result	The result as a `gsl::sf::result` object

Returns: Error code on failure

Definition at line 186 of file sf_exp.hpp.

◆ exp_mult()

double gsl::sf::exp_mult	(	double const	x,
		double const	y
	)

inline

C++ version of gsl_sf_exp_mult().

Exponentiate and multiply by a given factor: y * Exp(x)

Parameters

x	A real number
y	A real number

Returns: The function value

Definition at line 70 of file sf_exp.hpp.

◆ exp_mult_e()

int gsl::sf::exp_mult_e	(	double const	x,
		double const	y,
		result &	result
	)

inline

C++ version of gsl_sf_exp_mult_e().

Exponentiate and multiply by a given factor: y * Exp(x)

Parameters

x	A real number
y	A real number
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS or GSL_EUNDRFLW or GSL_EOVRFLW

Definition at line 61 of file sf_exp.hpp.

◆ exp_mult_e10_e()

int gsl::sf::exp_mult_e10_e	(	double const	x,
		double const	y,
		result_e10 &	result
	)

inline

C++ version of gsl_sf_exp_mult_e10_e().

Exponentiate and multiply by a given factor: y * Exp(x)

Parameters

x	A real number
y	A real number
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS or GSL_EUNDRFLW or GSL_EOVRFLW

Definition at line 80 of file sf_exp.hpp.

◆ exp_mult_err_e()

int gsl::sf::exp_mult_err_e	(	double const	x,
		double const	dx,
		double const	y,
		double const	dy,
		result &	result
	)

inline

C++ version of gsl_sf_exp_mult_err_e().

Exponentiate and multiply by a given factor: y * Exp(x), for quantities with associated errors.

Parameters

x	A real number
dx	A real number
y	A real number
dy	A real number
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS or GSL_EUNDRFLW or GSL_EOVRFLW

Definition at line 199 of file sf_exp.hpp.

◆ exp_mult_err_e10_e()

int gsl::sf::exp_mult_err_e10_e	(	double const	x,
		double const	dx,
		double const	y,
		double const	dy,
		result_e10 &	result
	)

inline

C++ version of gsl_sf_exp_mult_err_e10_e().

Exponentiate and multiply by a given factor: y * Exp(x), for quantities with associated errors.

Parameters

x	A real number
dx	A real number
y	A real number
dy	A real number
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS or GSL_EUNDRFLW or GSL_EOVRFLW

Definition at line 213 of file sf_exp.hpp.

◆ expint_3()

double gsl::sf::expint_3 ( double x )

inline

C++ version of gsl_sf_expint_3().

Ei_3(x) := Integral[ Exp[-t^3], {t,0,x}]

x >= 0.0

Parameters

x	A real number

Returns: The function value

Definition at line 247 of file sf_expint.hpp.

◆ expint_3_e()

int gsl::sf::expint_3_e	(	double const	x,
		result &	result
	)

inline

C++ version of gsl_sf_expint_3_e().

Ei_3(x) := Integral[ Exp[-t^3], {t,0,x}]

x >= 0.0

Parameters

x	A real number
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS or GSL_EDOM

Definition at line 238 of file sf_expint.hpp.

◆ expint_E1()

double gsl::sf::expint_E1 ( double const x )

inline

C++ version of gsl_sf_expint_E1().

E_1(x) := Re[ Integrate[ Exp[-xt]/t, {t,1,Infinity}] ]

x != 0.0

Parameters

x	A real number

Returns: The function value

Definition at line 47 of file sf_expint.hpp.

◆ expint_E1_e()

int gsl::sf::expint_E1_e	(	double	x,
		result &	result
	)

inline

C++ version of gsl_sf_expint_E1_e().

E_1(x) := Re[ Integrate[ Exp[-xt]/t, {t,1,Infinity}] ]

x != 0.0

Parameters

x	A real number
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS or GSL_EDOM or GSL_EOVRFLW or GSL_EUNDRFLW

Definition at line 38 of file sf_expint.hpp.

◆ expint_E1_scaled()

double gsl::sf::expint_E1_scaled ( double const x )

inline

C++ version of gsl_sf_expint_E1_scaled().

E_1_scaled(x) := exp(x) E_1(x)

x != 0.0

Parameters

x	A real number

Returns: The function value

Definition at line 108 of file sf_expint.hpp.

◆ expint_E1_scaled_e()

int gsl::sf::expint_E1_scaled_e	(	double const	x,
		result &	result
	)

inline

C++ version of gsl_sf_expint_E1_scaled_e().

E_1_scaled(x) := exp(x) E_1(x)

x != 0.0

Parameters

x	A real number
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS or GSL_EDOM or GSL_EOVRFLW or GSL_EUNDRFLW

Definition at line 98 of file sf_expint.hpp.

◆ expint_E2()

double gsl::sf::expint_E2 ( double const x )

inline

C++ version of gsl_sf_expint_E2().

E_2(x) := Re[ Integrate[ Exp[-xt]/t^2, {t,1,Infinity}] ]

x != 0.0

Parameters

x	A real number

Returns: The function value

Definition at line 66 of file sf_expint.hpp.

◆ expint_E2_e()

int gsl::sf::expint_E2_e	(	double const	x,
		result &	result
	)

inline

C++ version of gsl_sf_expint_E2_e().

E_2(x) := Re[ Integrate[ Exp[-xt]/t^2, {t,1,Infinity}] ]

x != 0.0

Parameters

x	A real number
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS or GSL_EDOM or GSL_EOVRFLW or GSL_EUNDRFLW

Definition at line 57 of file sf_expint.hpp.

◆ expint_E2_scaled()

double gsl::sf::expint_E2_scaled ( double const x )

inline

C++ version of gsl_sf_expint_E2_scaled().

E_2_scaled(x) := exp(x) E_2(x)

x != 0.0

Parameters

x	A real number

Returns: GSL_SUCCESS or GSL_EDOM or GSL_EOVRFLW or GSL_EUNDRFLW

Definition at line 128 of file sf_expint.hpp.

◆ expint_E2_scaled_e()

int gsl::sf::expint_E2_scaled_e	(	double const	x,
		result &	result
	)

inline

C++ version of gsl_sf_expint_E2_scaled_e().

E_2_scaled(x) := exp(x) E_2(x)

x != 0.0

Parameters

x	A real number
result	The result as a `gsl::sf::result` object

Returns: The function value

Definition at line 118 of file sf_expint.hpp.

◆ expint_Ei()

double gsl::sf::expint_Ei ( double const x )

inline

C++ version of gsl_sf_expint_Ei().

Ei(x) := - PV Integrate[ Exp[-t]/t, {t,-x,Infinity}] := PV Integrate[ Exp[t]/t, {t,-Infinity,x}]

x != 0.0

Parameters

x	A real number

Returns: GSL_SUCCESS or GSL_EDOM or GSL_EOVRFLW or GSL_EUNDRFLW

Definition at line 174 of file sf_expint.hpp.

◆ expint_Ei_e()

int gsl::sf::expint_Ei_e	(	double const	x,
		result &	result
	)

inline

C++ version of gsl_sf_expint_Ei_e().

Ei(x) := - PV Integrate[ Exp[-t]/t, {t,-x,Infinity}] := PV Integrate[ Exp[t]/t, {t,-Infinity,x}]

x != 0.0

Parameters

x	A real number
result	The result as a `gsl::sf::result` object

Returns: The function value

Definition at line 163 of file sf_expint.hpp.

◆ expint_Ei_scaled()

double gsl::sf::expint_Ei_scaled ( double const x )

inline

C++ version of gsl_sf_expint_Ei_scaled().

Ei_scaled(x) := exp(-x) Ei(x)

x != 0.0

Parameters

x	A real number

Returns: The function value

Definition at line 194 of file sf_expint.hpp.

◆ expint_Ei_scaled_e()

int gsl::sf::expint_Ei_scaled_e	(	double const	x,
		result &	result
	)

inline

C++ version of gsl_sf_expint_Ei_scaled_e().

Ei_scaled(x) := exp(-x) Ei(x)

x != 0.0

Parameters

x	A real number
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS or GSL_EDOM or GSL_EOVRFLW or GSL_EUNDRFLW

Definition at line 184 of file sf_expint.hpp.

◆ expint_En()

double gsl::sf::expint_En	(	int const	n,
		double const	x
	)

inline

C++ version of gsl_sf_expint_En().

E_n(x) := Re[ Integrate[ Exp[-xt]/t^n, {t,1,Infinity}] ]

x != 0.0

Parameters

n	An integer
x	A real number

Returns: The function value

Definition at line 88 of file sf_expint.hpp.

References gsl::rstat::n().

◆ expint_En_e()

int gsl::sf::expint_En_e	(	int const	n,
		double const	x,
		result &	result
	)

inline

C++ version of gsl_sf_expint_En_e().

E_n(x) := Re[ Integrate[ Exp[-xt]/t^n, {t,1,Infinity}] ]

x != 0.0

Parameters

n	An integer
x	A real number
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS or GSL_EDOM or GSL_EOVRFLW or GSL_EUNDRFLW

Definition at line 77 of file sf_expint.hpp.

References gsl::rstat::n().

◆ expint_En_scaled()

double gsl::sf::expint_En_scaled	(	int const	n,
		double const	x
	)

inline

C++ version of gsl_sf_expint_En_scaled().

E_n_scaled(x) := exp(x) E_n(x)

x != 0.0

Parameters

n	An integer
x	A real number

Returns: GSL_SUCCESS or GSL_EDOM or GSL_EOVRFLW or GSL_EUNDRFLW

Definition at line 151 of file sf_expint.hpp.

References gsl::rstat::n().

◆ expint_En_scaled_e()

int gsl::sf::expint_En_scaled_e	(	int const	n,
		double const	x,
		result &	result
	)

inline

C++ version of gsl_sf_expint_En_scaled_e().

E_n_scaled(x) := exp(x) E_n(x)

x != 0.0

Parameters

n	An integer
x	A real number
result	The result as a `gsl::sf::result` object

Returns: The function value

Definition at line 140 of file sf_expint.hpp.

References gsl::rstat::n().

◆ expm1()

double gsl::sf::expm1 ( double const x )

inline

C++ version of gsl_sf_expm1().

exp(x)-1

Parameters

x	A real number

Returns: The function value

Definition at line 97 of file sf_exp.hpp.

◆ expm1_e()

int gsl::sf::expm1_e	(	double const	x,
		result &	result
	)

inline

C++ version of gsl_sf_expm1_e().

exp(x)-1

Parameters

x	A real number
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS or GSL_EOVRFLW

Definition at line 89 of file sf_exp.hpp.

◆ exprel()

double gsl::sf::exprel ( double const x )

inline

C++ version of gsl_sf_exprel().

(exp(x)-1)/x = 1 + x/2 + x^2/(2*3) + x^3/(2*3*4) + ...

Parameters

x	A real number

Returns: The function value

Definition at line 113 of file sf_exp.hpp.

◆ exprel_2()

double gsl::sf::exprel_2 ( double const x )

inline

C++ version of gsl_sf_exprel_2().

2(exp(x)-1-x)/x^2 = 1 + x/3 + x^2/(3*4) + x^3/(3*4*5) + ...

Parameters

x	A real number

Returns: The function value

Definition at line 129 of file sf_exp.hpp.

◆ exprel_2_e()

int gsl::sf::exprel_2_e	(	double	x,
		result &	result
	)

inline

C++ version of gsl_sf_exprel_2_e().

2(exp(x)-1-x)/x^2 = 1 + x/3 + x^2/(3*4) + x^3/(3*4*5) + ...

Parameters

x	A real number
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS or GSL_EOVRFLW

Definition at line 121 of file sf_exp.hpp.

◆ exprel_e()

int gsl::sf::exprel_e	(	double const	x,
		result &	result
	)

inline

C++ version of gsl_sf_exprel_e().

(exp(x)-1)/x = 1 + x/2 + x^2/(2*3) + x^3/(2*3*4) + ...

Parameters

x	A real number
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS or GSL_EOVRFLW

Definition at line 105 of file sf_exp.hpp.

◆ exprel_n()

double gsl::sf::exprel_n	(	int const	n,
		double const	x
	)

inline

C++ version of gsl_sf_exprel_n().

Similarly for the N-th generalization of exprel_2. The so-called N-relative exponential

exprel_N(x) = N!/x^N (exp(x) - Sum[x^k/k!, {k,0,N-1}]) = 1 + x/(N+1) + x^2/((N+1)(N+2)) + ... = 1F1(1,1+N,x)

Parameters

n	A real number
x	A real number

Returns: The function value

Definition at line 157 of file sf_exp.hpp.

References gsl::rstat::n().

◆ exprel_n_CF_e()

int gsl::sf::exprel_n_CF_e	(	double const	n,
		double const	x,
		result &	result
	)

inline

C++ version of gsl_sf_exprel_n_CF_e().

Parameters

n	A real number
x	A real number
result	The result as a `gsl::sf::result` object

Returns: Error code on failure

Definition at line 166 of file sf_exp.hpp.

References gsl::rstat::n().

◆ exprel_n_e()

int gsl::sf::exprel_n_e	(	int const	n,
		double const	x,
		result &	result
	)

inline

C++ version of gsl_sf_exprel_n_e().

Similarly for the N-th generalization of exprel_2. The so-called N-relative exponential

exprel_N(x) = N!/x^N (exp(x) - Sum[x^k/k!, {k,0,N-1}]) = 1 + x/(N+1) + x^2/((N+1)(N+2)) + ... = 1F1(1,1+N,x)

Parameters

n	A real number
x	A real number
result	The result as a `gsl::sf::result` object

Returns: Error code on failure

Definition at line 143 of file sf_exp.hpp.

References gsl::rstat::n().

◆ fact()

double gsl::sf::fact ( unsigned int const n )

inline

C++ version of gsl_sf_fact().

n!

Parameters

n	An integer

Returns: The function value

Definition at line 191 of file sf_gamma.hpp.

References gsl::rstat::n().

◆ fact_e()

int gsl::sf::fact_e	(	unsigned int const	n,
		result &	result
	)

inline

C++ version of gsl_sf_fact_e().

n!

Parameters

n	An integer
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS or GSL_EDOM or GSL_EOVRFLW

Definition at line 183 of file sf_gamma.hpp.

References gsl::rstat::n().

◆ fermi_dirac_0()

double gsl::sf::fermi_dirac_0 ( double const x )

inline

C++ version of gsl_sf_fermi_dirac_0().

Complete integral F_0(x) = ln(1 + e^x)

Parameters

x	A real number

Returns: The function value

Definition at line 61 of file sf_fermi_dirac.hpp.

◆ fermi_dirac_0_e()

int gsl::sf::fermi_dirac_0_e	(	double const	x,
		result &	result
	)

inline

C++ version of gsl_sf_fermi_dirac_0_e().

Complete integral F_0(x) = ln(1 + e^x)

Parameters

x	A real number
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS or GSL_EUNDRFLW or GSL_EOVRFLW

Definition at line 53 of file sf_fermi_dirac.hpp.

◆ fermi_dirac_1()

double gsl::sf::fermi_dirac_1 ( double const x )

inline

C++ version of gsl_sf_fermi_dirac_1().

F_1(x): F_j(x) := 1/Gamma[j+1] Integral[ t^j /(Exp[t-x] + 1), {t,0,Infinity}]

Parameters

x	A real number

Returns: The function value

Definition at line 78 of file sf_fermi_dirac.hpp.

◆ fermi_dirac_1_e()

int gsl::sf::fermi_dirac_1_e	(	double const	x,
		result &	result
	)

inline

C++ version of gsl_sf_fermi_dirac_1_e().

F_1(x): F_j(x) := 1/Gamma[j+1] Integral[ t^j /(Exp[t-x] + 1), {t,0,Infinity}]

Parameters

x	A real number
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS or GSL_EUNDRFLW or GSL_EOVRFLW

Definition at line 70 of file sf_fermi_dirac.hpp.

◆ fermi_dirac_2()

double gsl::sf::fermi_dirac_2 ( double const x )

inline

C++ version of gsl_sf_fermi_dirac_2().

F_2(x): F_j(x) := 1/Gamma[j+1] Integral[ t^j /(Exp[t-x] + 1), {t,0,Infinity}]

Parameters

x	A real number

Returns: The function value

Definition at line 95 of file sf_fermi_dirac.hpp.

◆ fermi_dirac_2_e()

int gsl::sf::fermi_dirac_2_e	(	double const	x,
		result &	result
	)

inline

C++ version of gsl_sf_fermi_dirac_2_e().

F_2(x): F_j(x) := 1/Gamma[j+1] Integral[ t^j /(Exp[t-x] + 1), {t,0,Infinity}]

Parameters

x	A real number
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS or GSL_EUNDRFLW or GSL_EOVRFLW

Definition at line 87 of file sf_fermi_dirac.hpp.

◆ fermi_dirac_3half()

double gsl::sf::fermi_dirac_3half ( double const x )

inline

C++ version of gsl_sf_fermi_dirac_3half().

F_{3/2}(x): F_j(x) := 1/Gamma[j+1] Integral[ t^j /(Exp[t-x] + 1), {t,0,Infinity}]

Parameters

x	A real number

Returns: The function value

Definition at line 165 of file sf_fermi_dirac.hpp.

◆ fermi_dirac_3half_e()

int gsl::sf::fermi_dirac_3half_e	(	double const	x,
		result &	result
	)

inline

C++ version of gsl_sf_fermi_dirac_3half_e().

F_{3/2}(x): F_j(x) := 1/Gamma[j+1] Integral[ t^j /(Exp[t-x] + 1), {t,0,Infinity}]

Parameters

x	A real number
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS or GSL_EUNDRFLW or GSL_EOVRFLW

Definition at line 157 of file sf_fermi_dirac.hpp.

◆ fermi_dirac_half()

double gsl::sf::fermi_dirac_half ( double const x )

inline

C++ version of gsl_sf_fermi_dirac_half().

F_{1/2}(x): F_j(x) := 1/Gamma[j+1] Integral[ t^j /(Exp[t-x] + 1), {t,0,Infinity}]

Parameters

x	A real number

Returns: The function value

Definition at line 148 of file sf_fermi_dirac.hpp.

◆ fermi_dirac_half_e()

int gsl::sf::fermi_dirac_half_e	(	double const	x,
		result &	result
	)

inline

C++ version of gsl_sf_fermi_dirac_half_e().

F_{1/2}(x): F_j(x) := 1/Gamma[j+1] Integral[ t^j /(Exp[t-x] + 1), {t,0,Infinity}]

Parameters

x	A real number
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS or GSL_EUNDRFLW or GSL_EOVRFLW

Definition at line 140 of file sf_fermi_dirac.hpp.

◆ fermi_dirac_inc_0()

double gsl::sf::fermi_dirac_inc_0	(	double const	x,
		double const	b
	)

inline

C++ version of gsl_sf_fermi_dirac_inc_0().

Incomplete integral F_0(x,b) = ln(1 + e^(b-x)) - (b-x)

Parameters

x	A real number
b	A real number

Returns: The function value

Definition at line 184 of file sf_fermi_dirac.hpp.

References gsl::sf::mathieu::b().

◆ fermi_dirac_inc_0_e()

int gsl::sf::fermi_dirac_inc_0_e	(	double const	x,
		double const	b,
		result &	result
	)

inline

C++ version of gsl_sf_fermi_dirac_inc_0_e().

Incomplete integral F_0(x,b) = ln(1 + e^(b-x)) - (b-x)

Parameters

x	A real number
b	A real number
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS or GSL_EUNDRFLW or GSL_EDOM

Definition at line 175 of file sf_fermi_dirac.hpp.

References gsl::sf::mathieu::b().

◆ fermi_dirac_int()

double gsl::sf::fermi_dirac_int	(	int const	j,
		double const	x
	)

inline

C++ version of gsl_sf_fermi_dirac_int().

F_j(x) := 1/Gamma[j+1] Integral[ t^j /(Exp[t-x] + 1), {t,0,Infinity}]

Parameters

j	An integer
x	A real number

Returns: The function value

Definition at line 114 of file sf_fermi_dirac.hpp.

◆ fermi_dirac_int_e()

int gsl::sf::fermi_dirac_int_e	(	int const	j,
		double const	x,
		result &	result
	)

inline

C++ version of gsl_sf_fermi_dirac_int_e().

F_j(x) := 1/Gamma[j+1] Integral[ t^j /(Exp[t-x] + 1), {t,0,Infinity}]

Parameters

j	An integer
x	A real number
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS or GSL_EUNDRFLW or GSL_EOVRFLW

Definition at line 105 of file sf_fermi_dirac.hpp.

◆ fermi_dirac_m1()

double gsl::sf::fermi_dirac_m1 ( double const x )

inline

C++ version of gsl_sf_fermi_dirac_m1().

Complete integral F_{-1}(x) = e^x / (1 + e^x)

Parameters

x	A real number

Returns: The function value

Definition at line 44 of file sf_fermi_dirac.hpp.

◆ fermi_dirac_m1_e()

int gsl::sf::fermi_dirac_m1_e	(	double const	x,
		result &	result
	)

inline

C++ version of gsl_sf_fermi_dirac_m1_e().

Complete integral F_{-1}(x) = e^x / (1 + e^x)

Parameters

x	A real number
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS or GSL_EUNDRFLW

Definition at line 36 of file sf_fermi_dirac.hpp.

◆ fermi_dirac_mhalf()

double gsl::sf::fermi_dirac_mhalf ( double const x )

inline

C++ version of gsl_sf_fermi_dirac_mhalf().

F_{-1/2}(x): F_j(x) := 1/Gamma[j+1] Integral[ t^j /(Exp[t-x] + 1), {t,0,Infinity}]

Parameters

x	A real number

Returns: The function value

Definition at line 131 of file sf_fermi_dirac.hpp.

◆ fermi_dirac_mhalf_e()

int gsl::sf::fermi_dirac_mhalf_e	(	double const	x,
		result &	result
	)

inline

C++ version of gsl_sf_fermi_dirac_mhalf_e().

F_{-1/2}(x): F_j(x) := 1/Gamma[j+1] Integral[ t^j /(Exp[t-x] + 1), {t,0,Infinity}]

Parameters

x	A real number
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS or GSL_EUNDRFLW or GSL_EOVRFLW

Definition at line 123 of file sf_fermi_dirac.hpp.

◆ gamma()

double gsl::sf::gamma ( double const x )

inline

C++ version of gsl_sf_gamma().

Gamma(x), x not a negative integer Uses real Lanczos method.

Parameters

x	A real number

Returns: The function value

Definition at line 94 of file sf_gamma.hpp.

◆ gamma_e()

int gsl::sf::gamma_e	(	double const	x,
		result &	result
	)

inline

C++ version of gsl_sf_gamma_e().

Gamma(x), x not a negative integer Uses real Lanczos method.

Parameters

x	A real number
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS or GSL_EDOM or GSL_EOVRFLW or GSL_EROUND

Definition at line 85 of file sf_gamma.hpp.

◆ gamma_inc()

double gsl::sf::gamma_inc	(	double const	a,
		double const	x
	)

inline

C++ version of gsl_sf_gamma_inc().

Non-normalized Incomplete Gamma Function

Gamma(a,x) := Integral[ t^(a-1) e^(-t), {t,x,Infinity} ]

x >= 0.0 Gamma(a, 0) := Gamma(a)

Parameters

a	A real number
x	A real number

Returns: The function value

Definition at line 472 of file sf_gamma.hpp.

References gsl::sf::mathieu::a().

◆ gamma_inc_e()

int gsl::sf::gamma_inc_e	(	double const	a,
		double const	x,
		result &	result
	)

inline

C++ version of gsl_sf_gamma_inc_e().

Non-normalized Incomplete Gamma Function

Gamma(a,x) := Integral[ t^(a-1) e^(-t), {t,x,Infinity} ]

x >= 0.0 Gamma(a, 0) := Gamma(a)

Parameters

a	A real number
x	A real number
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS or GSL_EDOM

Definition at line 458 of file sf_gamma.hpp.

References gsl::sf::mathieu::a().

◆ gamma_inc_P()

double gsl::sf::gamma_inc_P	(	double const	a,
		double const	x
	)

inline

C++ version of gsl_sf_gamma_inc_P().

Complementary Normalized Incomplete Gamma Function

P(a,x) = 1/Gamma(a) Integral[ t^(a-1) e^(-t), {t,0,x} ]

a > 0, x >= 0

Parameters

a	A real number
x	A real number

Returns: The function value

Definition at line 443 of file sf_gamma.hpp.

References gsl::sf::mathieu::a().

◆ gamma_inc_P_e()

int gsl::sf::gamma_inc_P_e	(	double const	a,
		double const	x,
		result &	result
	)

inline

C++ version of gsl_sf_gamma_inc_P_e().

Complementary Normalized Incomplete Gamma Function

P(a,x) = 1/Gamma(a) Integral[ t^(a-1) e^(-t), {t,0,x} ]

a > 0, x >= 0

Parameters

a	A real number
x	A real number
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS or GSL_EDOM

Definition at line 430 of file sf_gamma.hpp.

References gsl::sf::mathieu::a().

◆ gamma_inc_Q()

double gsl::sf::gamma_inc_Q	(	double const	a,
		double const	x
	)

inline

C++ version of gsl_sf_gamma_inc_Q().

Normalized Incomplete Gamma Function

Q(a,x) = 1/Gamma(a) Integral[ t^(a-1) e^(-t), {t,x,Infinity} ]

a >= 0, x >= 0 Q(a,0) := 1 Q(0,x) := 0, x != 0

Parameters

a	A real number
x	A real number

Returns: The function value

Definition at line 416 of file sf_gamma.hpp.

References gsl::sf::mathieu::a().

◆ gamma_inc_Q_e()

int gsl::sf::gamma_inc_Q_e	(	double const	a,
		double const	x,
		result &	result
	)

inline

C++ version of gsl_sf_gamma_inc_Q_e().

Normalized Incomplete Gamma Function

Q(a,x) = 1/Gamma(a) Integral[ t^(a-1) e^(-t), {t,x,Infinity} ]

a >= 0, x >= 0 Q(a,0) := 1 Q(0,x) := 0, x != 0

Parameters

a	A real number
x	A real number
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS or GSL_EDOM

Definition at line 401 of file sf_gamma.hpp.

References gsl::sf::mathieu::a().

◆ gammainv()

double gsl::sf::gammainv ( double const x )

inline

C++ version of gsl_sf_gammainv().

1/Gamma(x) Uses real Lanczos method.

Parameters

x	A real number

Returns: The function value

Definition at line 132 of file sf_gamma.hpp.

◆ gammainv_e()

int gsl::sf::gammainv_e	(	double const	x,
		result &	result
	)

inline

C++ version of gsl_sf_gammainv_e().

1/Gamma(x) Uses real Lanczos method.

Parameters

x	A real number
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS or GSL_EUNDRFLW or GSL_EROUND

Definition at line 123 of file sf_gamma.hpp.

◆ gammastar()

double gsl::sf::gammastar ( double const x )

inline

C++ version of gsl_sf_gammastar().

Regulated Gamma Function, x > 0 Gamma^*(x) = Gamma(x)/(Sqrt[2Pi] x^(x-1/2) exp(-x)) = (1 + 1/(12x) + ...), x->Inf

Parameters

x	A real number

Returns: The function value

Definition at line 114 of file sf_gamma.hpp.

◆ gammastar_e()

int gsl::sf::gammastar_e	(	double const	x,
		result &	result
	)

inline

C++ version of gsl_sf_gammastar_e().

Regulated Gamma Function, x > 0 Gamma^*(x) = Gamma(x)/(Sqrt[2Pi] x^(x-1/2) exp(-x)) = (1 + 1/(12x) + ...), x->Inf

Parameters

x	A real number
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS or GSL_EDOM

Definition at line 104 of file sf_gamma.hpp.

◆ gegenpoly_1()

double gsl::sf::gegenpoly_1	(	double	lambda,
		double	x
	)

inline

C++ version of gsl_sf_gegenpoly_1().

Parameters

lambda	A real value greater than -0.5
x	A real value

Returns: The function value

Definition at line 62 of file sf_gegenbauer.hpp.

◆ gegenpoly_1_e()

int gsl::sf::gegenpoly_1_e	(	double	lambda,
		double	x,
		result &	result
	)

inline

C++ version of gsl_sf_gegenpoly_1_e().

Parameters

lambda	A real value greater than -0.5
x	A real value
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS

Definition at line 36 of file sf_gegenbauer.hpp.

◆ gegenpoly_2()

double gsl::sf::gegenpoly_2	(	double	lambda,
		double	x
	)

inline

C++ version of gsl_sf_gegenpoly_2().

Parameters

lambda	A real value greater than -0.5
x	A real value

Returns: The function value

Definition at line 70 of file sf_gegenbauer.hpp.

◆ gegenpoly_2_e()

int gsl::sf::gegenpoly_2_e	(	double	lambda,
		double	x,
		result &	result
	)

inline

C++ version of gsl_sf_gegenpoly_2_e().

Parameters

lambda	A real value greater than -0.5
x	A real value
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS

Definition at line 45 of file sf_gegenbauer.hpp.

◆ gegenpoly_3()

double gsl::sf::gegenpoly_3	(	double	lambda,
		double	x
	)

inline

C++ version of gsl_sf_gegenpoly_3().

Parameters

lambda	A real value greater than -0.5
x	A real value

Returns: The function value

Definition at line 78 of file sf_gegenbauer.hpp.

◆ gegenpoly_3_e()

int gsl::sf::gegenpoly_3_e	(	double	lambda,
		double	x,
		result &	result
	)

inline

C++ version of gsl_sf_gegenpoly_3_e().

Parameters

lambda	A real value greater than -0.5
x	A real value
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS

Definition at line 54 of file sf_gegenbauer.hpp.

◆ gegenpoly_array()

template<typename DATA >

int gsl::sf::gegenpoly_array	(	int	nmax,
		double	lambda,
		double	x,
		DATA &	result_array
	)

inline

C++ version of gsl_sf_gegenpoly_array().

Parameters

nmax	A nonnegative integer
lambda	A real value greater than -0.5
x	A real value
result_array	An array of size `nmax` + 1

Returns: GSL_SUCCESS or GSL_EDOM

Definition at line 121 of file sf_gegenbauer.hpp.

◆ gegenpoly_n()

double gsl::sf::gegenpoly_n	(	int	n,
		double	lambda,
		double	x
	)

inline

C++ version of gsl_sf_gegenpoly_n().

Parameters

n	A nonnegative integer
lambda	A real value greater than -0.5
x	A real value

Returns: The function value

Definition at line 97 of file sf_gegenbauer.hpp.

References gsl::rstat::n().

◆ gegenpoly_n_e()

int gsl::sf::gegenpoly_n_e	(	int	n,
		double	lambda,
		double	x,
		result &	result
	)

inline

C++ version of gsl_sf_gegenpoly_n_e().

Parameters

n	A nonnegative integer
lambda	A real value greater than -0.5
x	A real value
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS or GSL_EDOM

Definition at line 88 of file sf_gegenbauer.hpp.

References gsl::rstat::n().

◆ hazard()

double gsl::sf::hazard ( double x )

inline

C++ version of gsl_sf_hazard().

Hazard function, also known as the inverse Mill's ratio.

H(x) := Z(x)/Q(x) = Sqrt[2/Pi] Exp[-x^2 / 2] / Erfc[x/Sqrt[2]]

Parameters

x	A real number

Returns: The function value

Definition at line 134 of file sf_erf.hpp.

◆ hazard_e()

int gsl::sf::hazard_e	(	double	x,
		result &	result
	)

inline

C++ version of gsl_sf_hazard_e().

Hazard function, also known as the inverse Mill's ratio.

H(x) := Z(x)/Q(x) = Sqrt[2/Pi] Exp[-x^2 / 2] / Erfc[x/Sqrt[2]]

Parameters

x	A real number
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS or GSL_EUNDRFLW

Definition at line 123 of file sf_erf.hpp.

◆ hydrogenicR()

double gsl::sf::hydrogenicR	(	int const	n,
		int const	l,
		double const	Z,
		double const	r
	)

inline

C++ version of gsl_sf_hydrogenicR().

R_n := norm exp(-Z r/n) (2Z/n)^l Laguerre[n-l-1, 2l+1, 2Z/n r] normalization such that psi(n,l,r) = R_n Y_{lm}

Parameters

n	An integer
l	An integer
Z	A real value
r	A real value

Returns: The function value

Definition at line 73 of file sf_coulomb.hpp.

References gsl::rstat::n().

◆ hydrogenicR_1()

double gsl::sf::hydrogenicR_1	(	double const	Z,
		double const	r
	)

inline

C++ version of gsl_sf_hydrogenicR_1().

Normalized hydrogenic bound states, radial dependence. R_1 := 2Z sqrt(Z) exp(-Z r)

Parameters

Z	A real value
r	A real value

Returns: The function value

Definition at line 48 of file sf_coulomb.hpp.

◆ hydrogenicR_1_e()

int gsl::sf::hydrogenicR_1_e	(	double const	Z,
		double const	r,
		result &	result
	)

inline

C++ version of gsl_sf_hydrogenicR_1().

Normalized hydrogenic bound states, radial dependence. R_1 := 2Z sqrt(Z) exp(-Z r)

Parameters

Z	A real value
r	A real value
result	The result as a `gsl::sf::result` object

Returns: Error code on failure

Definition at line 38 of file sf_coulomb.hpp.

◆ hydrogenicR_e()

int gsl::sf::hydrogenicR_e	(	int const	n,
		int const	l,
		double const	Z,
		double const	r,
		result &	result
	)

inline

C++ version of gsl_sf_hydrogenicR_e().

R_n := norm exp(-Z r/n) (2Z/n)^l Laguerre[n-l-1, 2l+1, 2Z/n r] normalization such that psi(n,l,r) = R_n Y_{lm}

Parameters

n	An integer
l	an integer
Z	A real value
r	A real value
result	The result as a `gsl::sf::result` object

Returns: Error code on failure

Definition at line 61 of file sf_coulomb.hpp.

References gsl::rstat::n().

◆ hyperg_0F1()

double gsl::sf::hyperg_0F1	(	double const	c,
		double const	x
	)

inline

C++ version of gsl_sf_hyperg_0F1().

Hypergeometric function related to Bessel functions 0F1[c,x] = Gamma[c] x^(1/2(1-c)) I_{c-1}(2 Sqrt[x]) Gamma[c] (-x)^(1/2(1-c)) J_{c-1}(2 Sqrt[-x])

Parameters

c	A real value
x	A real value

Returns: The function value

Definition at line 52 of file sf_hyperg.hpp.

◆ hyperg_0F1_e()

int gsl::sf::hyperg_0F1_e	(	double	c,
		double	x,
		result &	result
	)

inline

C++ version of gsl_sf_hyperg_0F1_e().

Hypergeometric function related to Bessel functions 0F1[c,x] = Gamma[c] x^(1/2(1-c)) I_{c-1}(2 Sqrt[x]) Gamma[c] (-x)^(1/2(1-c)) J_{c-1}(2 Sqrt[-x])

Parameters

c	A real value
x	A real value
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS or GSL_EOVRFLW or GSL_EUNDRFLW

Definition at line 40 of file sf_hyperg.hpp.

◆ hyperg_1F1()

double gsl::sf::hyperg_1F1	(	double	a,
		double	b,
		double	x
	)

inline

C++ version of gsl_sf_hyperg_1F1().

Confluent hypergeometric function. 1F1[a,b,x] = M(a,b,x)

Parameters

a	A real value
b	A real value
x	A real value

Returns: The function value

Definition at line 98 of file sf_hyperg.hpp.

References gsl::sf::mathieu::a(), and gsl::sf::mathieu::b().

◆ hyperg_1F1_e()

int gsl::sf::hyperg_1F1_e	(	double const	a,
		double const	b,
		double const	x,
		result &	result
	)

inline

C++ version of gsl_sf_hyperg_1F1_e().

Confluent hypergeometric function. 1F1[a,b,x] = M(a,b,x)

Parameters

a	A real value
b	A real value
x	A real value
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS

Definition at line 87 of file sf_hyperg.hpp.

References gsl::sf::mathieu::a(), and gsl::sf::mathieu::b().

◆ hyperg_1F1_int()

double gsl::sf::hyperg_1F1_int	(	int const	m,
		int const	n,
		double	x
	)

inline

C++ version of gsl_sf_hyperg_1F1_int().

Confluent hypergeometric function for integer parameters. 1F1[m,n,x] = M(m,n,x)

Parameters

m	An integer
n	An integer
x	A real value

Returns: The function value

Definition at line 75 of file sf_hyperg.hpp.

References gsl::rstat::n().

◆ hyperg_1F1_int_e()

int gsl::sf::hyperg_1F1_int_e	(	int const	m,
		int const	n,
		double const	x,
		result &	result
	)

inline

C++ version of gsl_sf_hyperg_1F1_int_e().

Confluent hypergeometric function for integer parameters. 1F1[m,n,x] = M(m,n,x)

Parameters

m	An integer
n	An integer
x	A real value
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS

Definition at line 64 of file sf_hyperg.hpp.

References gsl::rstat::n().

◆ hyperg_2F0()

double gsl::sf::hyperg_2F0	(	double const	a,
		double const	b,
		double const	x
	)

inline

C++ version of gsl_sf_hyperg_2F0().

Mysterious hypergeometric function. The series representation is a divergent hypergeometric series. However, for x < 0 we have 2F0(a,b,x) = (-1/x)^a U(a,1+a-b,-1/x)

Parameters

a	A real value
b	A real value
x	A real value

Returns: The function value

Definition at line 298 of file sf_hyperg.hpp.

References gsl::sf::mathieu::a(), and gsl::sf::mathieu::b().

◆ hyperg_2F0_e()

int gsl::sf::hyperg_2F0_e	(	double const	a,
		double const	b,
		double const	x,
		result &	result
	)

inline

C++ version of gsl_sf_hyperg_2F0_e().

Mysterious hypergeometric function. The series representation is a divergent hypergeometric series. However, for x < 0 we have 2F0(a,b,x) = (-1/x)^a U(a,1+a-b,-1/x)

Parameters

a	A real value
b	A real value
x	A real value
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS or GSL_EDOM

Definition at line 286 of file sf_hyperg.hpp.

References gsl::sf::mathieu::a(), and gsl::sf::mathieu::b().

◆ hyperg_2F1()

double gsl::sf::hyperg_2F1	(	double	a,
		double	b,
		double	c,
		double	x
	)

inline

C++ version of gsl_sf_hyperg_2F1().

Gauss hypergeometric function 2F1[a,b,c,x] |x| < 1

Parameters

a	A real value
b	A real value
c	A real value
x	A real value

Returns: The function value

Definition at line 193 of file sf_hyperg.hpp.

References gsl::sf::mathieu::a(), and gsl::sf::mathieu::b().

◆ hyperg_2F1_conj()

double gsl::sf::hyperg_2F1_conj	(	double	aR,
		double	aI,
		double	c,
		double	x
	)

inline

C++ version of gsl_sf_hyperg_2F1_conj().

Gauss hypergeometric function 2F1[aR + I aI, aR - I aI, c, x]

Parameters

aR	Real part of a complex number
aI	Imaginary part of a complex number
c	A real value
x	A real value

Returns: The function value

Definition at line 218 of file sf_hyperg.hpp.

◆ hyperg_2F1_conj_e()

int gsl::sf::hyperg_2F1_conj_e	(	double const	aR,
		double const	aI,
		double const	c,
		double const	x,
		result &	result
	)

inline

C++ version of gsl_sf_hyperg_2F1_conj_e().

Gauss hypergeometric function 2F1[aR + I aI, aR - I aI, c, x]

Parameters

aR	Real part of a complex number
aI	Imaginary part of a complex number
c	A real value
x	A real value
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS

Definition at line 206 of file sf_hyperg.hpp.

◆ hyperg_2F1_conj_renorm()

double gsl::sf::hyperg_2F1_conj_renorm	(	double	aR,
		double	aI,
		double	c,
		double	x
	)

inline

C++ version of gsl_sf_hyperg_2F1_conj_renorm().

Renormalized Gauss hypergeometric function 2F1[aR + I aI, aR - I aI, c, x] / Gamma[c] |x| < 1

Parameters

aR	Real part of a complex number
aI	Imaginary part of a complex number
c	A real value
x	A real value

Returns: The function value

Definition at line 273 of file sf_hyperg.hpp.

◆ hyperg_2F1_conj_renorm_e()

int gsl::sf::hyperg_2F1_conj_renorm_e	(	double const	aR,
		double const	aI,
		double const	c,
		double const	x,
		result &	result
	)

inline

C++ version of gsl_sf_hyperg_2F1_conj_renorm_e().

Renormalized Gauss hypergeometric function 2F1[aR + I aI, aR - I aI, c, x] / Gamma[c] |x| < 1

Parameters

aR	Real part of a complex number
aI	Imaginary part of a complex number
c	A real value
x	A real value
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS

Definition at line 259 of file sf_hyperg.hpp.

◆ hyperg_2F1_e()

int gsl::sf::hyperg_2F1_e	(	double	a,
		double	b,
		double const	c,
		double const	x,
		result &	result
	)

inline

C++ version of gsl_sf_hyperg_2F1_e().

Gauss hypergeometric function 2F1[a,b,c,x] |x| < 1

Parameters

a	A real value
b	A real value
c	A real value
x	A real value
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS

Definition at line 181 of file sf_hyperg.hpp.

References gsl::sf::mathieu::a(), and gsl::sf::mathieu::b().

◆ hyperg_2F1_renorm()

double gsl::sf::hyperg_2F1_renorm	(	double	a,
		double	b,
		double	c,
		double	x
	)

inline

C++ version of gsl_sf_hyperg_2F1_renorm().

Renormalized Gauss hypergeometric function 2F1[a,b,c,x] / Gamma[c] |x| < 1

Parameters

a	A real value
b	A real value
c	A real value
x	A real value

Returns: The function value

Definition at line 245 of file sf_hyperg.hpp.

References gsl::sf::mathieu::a(), and gsl::sf::mathieu::b().

◆ hyperg_2F1_renorm_e()

int gsl::sf::hyperg_2F1_renorm_e	(	double const	a,
		double const	b,
		double const	c,
		double const	x,
		result &	result
	)

inline

C++ version of gsl_sf_hyperg_2F1_renorm_e().

Renormalized Gauss hypergeometric function 2F1[a,b,c,x] / Gamma[c] |x| < 1

Parameters

a	A real value
b	A real value
c	A real value
x	A real value
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS

Definition at line 232 of file sf_hyperg.hpp.

References gsl::sf::mathieu::a(), and gsl::sf::mathieu::b().

◆ hyperg_U()

double gsl::sf::hyperg_U	(	double const	a,
		double const	b,
		double const	x
	)

inline

C++ version of gsl_sf_hyperg_U().

Confluent hypergeometric function. U(a,b,x)

Parameters

a	A real value
b	A real value
x	A real value

Returns: The function value

Definition at line 156 of file sf_hyperg.hpp.

References gsl::sf::mathieu::a(), and gsl::sf::mathieu::b().

◆ hyperg_U_e()

int gsl::sf::hyperg_U_e	(	double const	a,
		double const	b,
		double const	x,
		result &	result
	)

inline

C++ version of gsl_sf_hyperg_U_e().

Confluent hypergeometric function. U(a,b,x)

Parameters

a	A real value
b	A real value
x	A real value
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS

Definition at line 145 of file sf_hyperg.hpp.

References gsl::sf::mathieu::a(), and gsl::sf::mathieu::b().

◆ hyperg_U_e10_e()

int gsl::sf::hyperg_U_e10_e	(	double const	a,
		double const	b,
		double const	x,
		result_e10 &	result
	)

inline

C++ version of gsl_sf_hyperg_U_e10_e().

Confluent hypergeometric function. U(a,b,x)

Parameters

a	A real value
b	A real value
x	A real value
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS

Definition at line 168 of file sf_hyperg.hpp.

References gsl::sf::mathieu::a(), and gsl::sf::mathieu::b().

◆ hyperg_U_int()

double gsl::sf::hyperg_U_int	(	int const	m,
		int const	n,
		double const	x
	)

inline

C++ version of gsl_sf_hyperg_U_int().

Confluent hypergeometric function for integer parameters. U(m,n,x)

Parameters

m	An integer
n	An integer
x	A real value

Returns: The function value

Definition at line 121 of file sf_hyperg.hpp.

References gsl::rstat::n().

◆ hyperg_U_int_e()

int gsl::sf::hyperg_U_int_e	(	int const	m,
		int const	n,
		double const	x,
		result &	result
	)

inline

C++ version of gsl_sf_hyperg_U_int_e().

Confluent hypergeometric function for integer parameters. U(m,n,x)

Parameters

m	An integer
n	An integer
x	A real value
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS

Definition at line 110 of file sf_hyperg.hpp.

References gsl::rstat::n().

◆ hyperg_U_int_e10_e()

int gsl::sf::hyperg_U_int_e10_e	(	int const	m,
		int const	n,
		double const	x,
		result_e10 &	result
	)

inline

C++ version of gsl_sf_hyperg_U_int_e10_e().

Confluent hypergeometric function for integer parameters. U(m,n,x)

Parameters

m	An integer
n	An integer
x	A real value
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS

Definition at line 133 of file sf_hyperg.hpp.

References gsl::rstat::n().

◆ hypot()

double gsl::sf::hypot	(	double const	x,
		double const	y
	)

inline

C++ version of gsl_sf_hypot().

Parameters

x	A real value
y	A real value

Returns: The function value

Definition at line 70 of file sf_trig.hpp.

◆ hypot_e()

int gsl::sf::hypot_e	(	double const	x,
		double const	y,
		result &	result
	)

inline

C++ version of gsl_sf_hypot_e().

Parameters

x	A real value
y	A real value
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS

Definition at line 62 of file sf_trig.hpp.

◆ hzeta()

double gsl::sf::hzeta	(	double const	s,
		double const	q
	)

inline

C++ version of gsl_sf_hzeta().

Hurwitz Zeta Function zeta(s,q) = Sum[ (k+q)^(-s), {k,0,Infinity} ]

s > 1.0, q > 0.0

Parameters

s	A real value
q	A real value

Returns: The function value

Definition at line 144 of file sf_zeta.hpp.

◆ hzeta_e()

int gsl::sf::hzeta_e	(	double const	s,
		double const	q,
		result &	result
	)

inline

C++ version of gsl_sf_hzeta_e().

Hurwitz Zeta Function zeta(s,q) = Sum[ (k+q)^(-s), {k,0,Infinity} ]

s > 1.0, q > 0.0

Parameters

s	A real value
q	A real value
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS or GSL_EDOM or GSL_EUNDRFLW or GSL_EOVRFLW

Definition at line 132 of file sf_zeta.hpp.

◆ laguerre_1()

double gsl::sf::laguerre_1	(	double	a,
		double	x
	)

inline

C++ version of gsl_sf_laguerre_1().

L^a_n(x) = (a+1)_n / n! 1F1(-n,a+1,x)

Parameters

a	A real value
x	A real value

Returns: The function value

Definition at line 66 of file sf_laguerre.hpp.

References gsl::sf::mathieu::a().

◆ laguerre_1_e()

int gsl::sf::laguerre_1_e	(	double const	a,
		double const	x,
		result &	result
	)

inline

C++ version of gsl_sf_laguerre_1_e().

L^a_n(x) = (a+1)_n / n! 1F1(-n,a+1,x)

Parameters

a	A real value
x	A real value
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS

Definition at line 37 of file sf_laguerre.hpp.

References gsl::sf::mathieu::a().

◆ laguerre_2()

double gsl::sf::laguerre_2	(	double	a,
		double	x
	)

inline

C++ version of gsl_sf_laguerre_2().

L^a_n(x) = (a+1)_n / n! 1F1(-n,a+1,x)

Parameters

a	A real value
x	A real value

Returns: The function value

Definition at line 74 of file sf_laguerre.hpp.

References gsl::sf::mathieu::a().

◆ laguerre_2_e()

int gsl::sf::laguerre_2_e	(	double const	a,
		double const	x,
		result &	result
	)

inline

C++ version of gsl_sf_laguerre_2_e().

L^a_n(x) = (a+1)_n / n! 1F1(-n,a+1,x)

Parameters

a	A real value
x	A real value
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS

Definition at line 47 of file sf_laguerre.hpp.

References gsl::sf::mathieu::a().

◆ laguerre_3()

double gsl::sf::laguerre_3	(	double	a,
		double	x
	)

inline

C++ version of gsl_sf_laguerre_3().

L^a_n(x) = (a+1)_n / n! 1F1(-n,a+1,x)

Parameters

a	A real value
x	A real value

Returns: The function value

Definition at line 82 of file sf_laguerre.hpp.

References gsl::sf::mathieu::a().

◆ laguerre_3_e()

int gsl::sf::laguerre_3_e	(	double const	a,
		double const	x,
		result &	result
	)

inline

C++ version of gsl_sf_laguerre_3_e().

L^a_n(x) = (a+1)_n / n! 1F1(-n,a+1,x)

Parameters

a	A real value
x	A real value
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS

Definition at line 57 of file sf_laguerre.hpp.

References gsl::sf::mathieu::a().

◆ laguerre_n()

double gsl::sf::laguerre_n	(	int	n,
		double	a,
		double	x
	)

inline

C++ version of gsl_sf_laguerre_n().

Evaluate generalized Laguerre polynomials.

a > -1.0 n >= 0

Parameters

n	An integer
a	A real value
x	A real value

Returns: The function value

Definition at line 108 of file sf_laguerre.hpp.

References gsl::sf::mathieu::a(), and gsl::rstat::n().

◆ laguerre_n_e()

int gsl::sf::laguerre_n_e	(	int const	n,
		double const	a,
		double const	x,
		result &	result
	)

inline

C++ version of gsl_sf_laguerre_n_e().

Evaluate generalized Laguerre polynomials.

a > -1.0 n >= 0

Parameters

n	An integer
a	A real value
x	A real value
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS or GSL_EDOM

Definition at line 95 of file sf_laguerre.hpp.

References gsl::sf::mathieu::a(), and gsl::rstat::n().

◆ lnbeta()

double gsl::sf::lnbeta	(	double const	a,
		double const	b
	)

inline

C++ version of gsl_sf_lnbeta().

Logarithm of Beta Function Log[B(a,b)]

a > 0, b > 0

Parameters

a	A real number
b	A real number

Returns: The function value

Definition at line 497 of file sf_gamma.hpp.

References gsl::sf::mathieu::a(), and gsl::sf::mathieu::b().

◆ lnbeta_e()

int gsl::sf::lnbeta_e	(	double const	a,
		double const	b,
		result &	result
	)

inline

C++ version of gsl_sf_lnbeta_e().

Logarithm of Beta Function Log[B(a,b)]

a > 0, b > 0

Parameters

a	A real number
b	A real number
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS or GSL_EDOM

Definition at line 485 of file sf_gamma.hpp.

References gsl::sf::mathieu::a(), and gsl::sf::mathieu::b().

◆ lnbeta_sgn_e()

int gsl::sf::lnbeta_sgn_e	(	double const	x,
		double const	y,
		result &	result,
		double &	sgn
	)

inline

C++ version of gsl_sf_lnbeta_sgn_e().

Logarithm of Beta Function Log[B(a,b)]

a > 0, b > 0

Parameters

x	A real number
y	A real number
result	The result as a `gsl::sf::result` object
sgn	Record the sign here

Returns: GSL_SUCCESS or GSL_EDOM

Definition at line 527 of file sf_gamma.hpp.

◆ lnchoose()

double gsl::sf::lnchoose	(	unsigned int	n,
		unsigned int	m
	)

inline

C++ version of gsl_sf_lnchoose().

log(n choose m)

Parameters

n	An integer
m	An integer

Returns: The function value

Definition at line 260 of file sf_gamma.hpp.

References gsl::rstat::n().

◆ lnchoose_e()

int gsl::sf::lnchoose_e	(	unsigned int	n,
		unsigned int	m,
		result &	result
	)

inline

C++ version of gsl_sf_lnchoose_e().

log(n choose m)

Parameters

n	An integer
m	An integer
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS or GSL_EDOM

Definition at line 251 of file sf_gamma.hpp.

References gsl::rstat::n().

◆ lncosh()

double gsl::sf::lncosh ( double const x )

inline

C++ version of gsl_sf_lncosh().

Log(Cosh(x))

Parameters

x	A real value

Returns: The function value

Definition at line 145 of file sf_trig.hpp.

◆ lncosh_e()

int gsl::sf::lncosh_e	(	double const	x,
		result &	result
	)

inline

C++ version of gsl_sf_lncosh_e().

Log(Cosh(x))

Parameters

x	A real value
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS

Definition at line 138 of file sf_trig.hpp.

◆ lndoublefact()

double gsl::sf::lndoublefact ( unsigned int const n )

inline

C++ version of gsl_sf_lndoublefact().

log(n!!)

Parameters

n	An integer

Returns: The function value

Definition at line 241 of file sf_gamma.hpp.

References gsl::rstat::n().

◆ lndoublefact_e()

int gsl::sf::lndoublefact_e	(	unsigned int const	n,
		result &	result
	)

inline

C++ version of gsl_sf_lndoublefact_e().

log(n!!)

Parameters

n	An integer
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS

Definition at line 233 of file sf_gamma.hpp.

References gsl::rstat::n().

◆ lnfact()

double gsl::sf::lnfact ( unsigned int const n )

inline

C++ version of gsl_sf_lnfact().

log(n!) Faster than ln(Gamma(n+1)) for n < 170; defers for larger n.

Parameters

n	An integer

Returns: The function value

Definition at line 225 of file sf_gamma.hpp.

References gsl::rstat::n().

◆ lnfact_e()

int gsl::sf::lnfact_e	(	unsigned int const	n,
		result &	result
	)

inline

C++ version of gsl_sf_lnfact_e().

log(n!) Faster than ln(Gamma(n+1)) for n < 170; defers for larger n.

Parameters

n	An integer
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS

Definition at line 216 of file sf_gamma.hpp.

References gsl::rstat::n().

◆ lngamma()

double gsl::sf::lngamma ( double const x )

inline

C++ version of gsl_sf_lngamma().

Log[Gamma(x)], x not a negative integer Uses real Lanczos method. Returns the real part of Log[Gamma[x]] when x < 0, i.e. Log[|Gamma[x]|].

Parameters

x	A real number

Returns: The function value

Definition at line 50 of file sf_gamma.hpp.

◆ lngamma_complex_e()

int gsl::sf::lngamma_complex_e	(	double	zr,
		double	zi,
		result &	lnr,
		result &	arg
	)

inline

C++ version of gsl_sf_lngamma_complex_e().

Log[Gamma(z)] for z complex, z not a negative integer Uses complex Lanczos method. Note that the phase part (arg) is not well-determined when |z| is very large, due to inevitable roundoff in restricting to (-Pi,Pi]. This will raise the GSL_ELOSS exception when it occurs. The absolute value part (lnr), however, never suffers.

Calculates: lnr = log|Gamma(z)| arg = arg(Gamma(z)) in (-Pi, Pi]

Parameters

zr	The real part
zi	The imaginary part
lnr	Result as a `gsl::sf::result` object
arg	Result as a `gsl::sf::result` object

Returns: GSL_SUCCESS or GSL_EDOM or GSL_ELOSS

Definition at line 151 of file sf_gamma.hpp.

References gsl::cpx::arg().

◆ lngamma_e()

int gsl::sf::lngamma_e	(	double	x,
		result &	result
	)

inline

C++ version of gsl_sf_lngamma_e().

Log[Gamma(x)], x not a negative integer Uses real Lanczos method. Returns the real part of Log[Gamma[x]] when x < 0, i.e. Log[|Gamma[x]|].

Parameters

x	A real number
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS or GSL_EDOM or GSL_EROUND

Definition at line 39 of file sf_gamma.hpp.

◆ lngamma_sgn_e()

int gsl::sf::lngamma_sgn_e	(	double	x,
		result &	result_lg,
		double &	sgn
	)

inline

C++ version of gsl_sf_lngamma_sgn_e().

Log[Gamma(x)], x not a negative integer Uses real Lanczos method. Returns the real part of Log[Gamma[x]] when x < 0,

Parameters

x	A real number
result_lg	Result as a `gsl::sf::result` object
sgn	The sign as a return value

Returns: GSL_SUCCESS or GSL_EDOM or GSL_EROUND

Definition at line 75 of file sf_gamma.hpp.

◆ lnpoch()

double gsl::sf::lnpoch	(	double const	a,
		double const	x
	)

inline

C++ version of gsl_sf_lnpoch().

Logarithm of Pochhammer (Apell) symbol log( (a)_x ) where (a)_x := Gamma[a + x]/Gamma[a]

a > 0, a+x > 0

Parameters

a	A real number
x	A real number

Returns: The function value

Definition at line 305 of file sf_gamma.hpp.

References gsl::sf::mathieu::a().

◆ lnpoch_e()

int gsl::sf::lnpoch_e	(	double const	a,
		double const	x,
		result &	result
	)

inline

C++ version of gsl_sf_lnpoch_e().

Logarithm of Pochhammer (Apell) symbol log( (a)_x ) where (a)_x := Gamma[a + x]/Gamma[a]

a > 0, a+x > 0

Parameters

a	A real number
x	A real number
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS or GSL_EDOM

Definition at line 292 of file sf_gamma.hpp.

References gsl::sf::mathieu::a().

◆ lnpoch_sgn_e()

int gsl::sf::lnpoch_sgn_e	(	double const	a,
		double const	x,
		result &	result,
		double &	sgn
	)

inline

C++ version of gsl_sf_lnpoch_sgn_e().

Logarithm of Pochhammer (Apell) symbol, with sign information. result = log( |(a)_x| ) sgn = sgn( (a)_x ) where (a)_x := Gamma[a + x]/Gamma[a]

a != neg integer, a+x != neg integer

Parameters

a	A real number
x	A real number
result	The result as a `gsl::sf::result` object
sgn	Record the sign here

Returns: GSL_SUCCESS or GSL_EDOM

Definition at line 339 of file sf_gamma.hpp.

◆ lnsinh()

double gsl::sf::lnsinh ( double const x )

inline

C++ version of gsl_sf_lnsinh().

Log(Sinh(x)), x > 0

Parameters

x	A real value

Returns: The function value

Definition at line 130 of file sf_trig.hpp.

◆ lnsinh_e()

int gsl::sf::lnsinh_e	(	double const	x,
		result &	result
	)

inline

C++ version of gsl_sf_lnsinh_e().

Log(Sinh(x)), x > 0

Parameters

x	A real value
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS or GSL_EDOM

Definition at line 123 of file sf_trig.hpp.

◆ log()

double gsl::sf::log ( double const x )

inline

C++ version of gsl_sf_log().

Parameters

x	A real value

Returns: The function value

Definition at line 41 of file sf_log.hpp.

◆ log_1plusx()

double gsl::sf::log_1plusx ( double const x )

inline

C++ version of gsl_sf_log_1plusx().

Log(1 + x)

Parameters

x	A real value

Returns: The function value

Definition at line 85 of file sf_log.hpp.

◆ log_1plusx_e()

int gsl::sf::log_1plusx_e	(	double const	x,
		result &	result
	)

inline

C++ version of gsl_sf_log_1plusx_e().

Log(1 + x)

Parameters

x	A real value
result	The result as a `gs::sf::result` object

Returns: GSL_SUCCESS or GSL_EDOM

Definition at line 78 of file sf_log.hpp.

◆ log_1plusx_mx()

double gsl::sf::log_1plusx_mx ( double const x )

inline

C++ version of gsl_sf_log_1plusx_mx().

Log(1 + x) - x

Parameters

x	A real value

Returns: The function value

Definition at line 101 of file sf_log.hpp.

◆ log_1plusx_mx_e()

int gsl::sf::log_1plusx_mx_e	(	double const	x,
		result &	result
	)

inline

C++ version of gsl_sf_log_1plusx_mx_e().

Log(1 + x) - x

Parameters

x	A real value
result	The result as a `gs::sf::result` object

Returns: GSL_SUCCESS or GSL_EDOM

Definition at line 93 of file sf_log.hpp.

◆ log_abs()

double gsl::sf::log_abs ( double const x )

inline

C++ version of gsl_sf_log_abs().

Log(|x|)

Parameters

x	A real value

Returns: The function value

Definition at line 57 of file sf_log.hpp.

◆ log_abs_e()

int gsl::sf::log_abs_e	(	double const	x,
		result &	result
	)

inline

C++ version of gsl_sf_log_abs_e().

Log(|x|)

Parameters

x	A real value
result	The result as a `gs::sf::result` object

Returns: GSL_SUCCESS or GSL_EDOM

Definition at line 49 of file sf_log.hpp.

◆ log_e()

int gsl::sf::log_e	(	double const	x,
		result &	result
	)

inline

C++ version of gsl_sf_log_e().

Parameters

x	A real value
result	The result as a `gs::sf::result` object

Returns: GSL_SUCCESS or GSL_EDOM

Definition at line 35 of file sf_log.hpp.

◆ log_erfc()

double gsl::sf::log_erfc ( double x )

inline

C++ version of gsl_sf_log_erfc().

Log Complementary Error Function

Parameters

x	A real number

Returns: The function value

Definition at line 60 of file sf_erf.hpp.

◆ log_erfc_e()

int gsl::sf::log_erfc_e	(	double	x,
		result &	result
	)

inline

C++ version of gsl_sf_log_erfc_e().

Log Complementary Error Function

Parameters

x	A real number
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS

Definition at line 53 of file sf_erf.hpp.

◆ multiply()

double gsl::sf::multiply	(	double const	x,
		double const	y
	)

inline

C++ version of gsl_sf_multiply().

Parameters

x	A real number
y	Another real number

Returns: GSL_SUCCESS or GSL_EOVRFLW or GSL_EUNDRFLW

Definition at line 44 of file sf_elementary.hpp.

◆ multiply_e()

int gsl::sf::multiply_e	(	double const	x,
		double const	y,
		result &	result
	)

inline

C++ version of gsl_sf_multiply_e().

Parameters

x	A real number
y	Another real number
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS or GSL_EOVRFLW or GSL_EUNDRFLW

Definition at line 36 of file sf_elementary.hpp.

◆ multiply_err_e()

int gsl::sf::multiply_err_e	(	double const	x,
		double const	dx,
		double const	y,
		double const	dy,
		result &	result
	)

inline

C++ version of gsl_sf_multiply_err_e().

Parameters

x	A real number
dx	Error in x
y	Another real number
dy	Error in y
result	The result as a `gsl::sf::result` object

Returns: Error code on failure

Definition at line 54 of file sf_elementary.hpp.

◆ poch()

double gsl::sf::poch	(	double const	a,
		double const	x
	)

inline

C++ version of gsl_sf_poch().

Pochhammer (Apell) symbol (a)_x := Gamma[a + x]/Gamma[x]

a != neg integer, a+x != neg integer

Parameters

a	A real number
x	A real number

Returns: The function value

Definition at line 364 of file sf_gamma.hpp.

References gsl::sf::mathieu::a().

◆ poch_e()

int gsl::sf::poch_e	(	double const	a,
		double const	x,
		result &	result
	)

inline

C++ version of gsl_sf_poch_e().

Pochhammer (Apell) symbol (a)_x := Gamma[a + x]/Gamma[x]

a != neg integer, a+x != neg integer

Parameters

a	A real number
x	A real number
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS or GSL_EDOM or GSL_EOVRFLW

Definition at line 352 of file sf_gamma.hpp.

References gsl::sf::mathieu::a().

◆ pochrel()

double gsl::sf::pochrel	(	double const	a,
		double const	x
	)

inline

C++ version of gsl_sf_pochrel().

Relative Pochhammer (Apell) symbol ((a,x) - 1)/x where (a,x) = (a)_x := Gamma[a + x]/Gamma[a]

Parameters

a	A real number
x	A real number

Returns: The function value

Definition at line 386 of file sf_gamma.hpp.

References gsl::sf::mathieu::a().

◆ pochrel_e()

int gsl::sf::pochrel_e	(	double const	a,
		double const	x,
		result &	result
	)

inline

C++ version of gsl_sf_pochrel_e().

Relative Pochhammer (Apell) symbol ((a,x) - 1)/x where (a,x) = (a)_x := Gamma[a + x]/Gamma[a]

Parameters

a	A real number
x	A real number
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS or GSL_EDOM

Definition at line 375 of file sf_gamma.hpp.

References gsl::sf::mathieu::a().

◆ polar_to_rect()

int gsl::sf::polar_to_rect	(	double const	r,
		double const	theta,
		result &	x,
		result &	y
	)

inline

C++ version of gsl_sf_polar_to_rect().

Parameters

r	A real value (distance)
theta	A real value (angle)
x	A real value
y	A real value

Returns: GSL_SUCCESS

Definition at line 154 of file sf_trig.hpp.

◆ pow_int()

double gsl::sf::pow_int	(	double const	x,
		int const	n
	)

inline

C++ version of gsl_sf_pow_int().

Parameters

x	A real value
n	An integer

Returns: The nth power of x

Definition at line 43 of file sf_pow_int.hpp.

References gsl::rstat::n().

◆ pow_int_e()

int gsl::sf::pow_int_e	(	double	x,
		int	n,
		result &	result
	)

inline

C++ version of gsl_sf_pow_int_e().

Parameters

x	A real value
n	An integer
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS

Definition at line 36 of file sf_pow_int.hpp.

References gsl::rstat::n().

◆ psi()

double gsl::sf::psi ( double const x )

inline

C++ version of gsl_sf_psi().

Poly-Gamma Functions

psi(m,x) := (d/dx)^m psi(0,x) = (d/dx)^{m+1} log(gamma(x))

Di-Gamma Function psi(x) = psi(0, x)

x != 0.0, -1.0, -2.0, ...

Parameters

x	A real value

Returns: The function value

Definition at line 82 of file sf_psi.hpp.

◆ psi_1()

double gsl::sf::psi_1 ( double const x )

inline

C++ version of gsl_sf_psi_1().

Poly-Gamma Functions

psi(m,x) := (d/dx)^m psi(0,x) = (d/dx)^{m+1} log(gamma(x))

Tri-Gamma Function psi^(1)(n)

n > 0

Parameters

x	A real value

Returns: The function value

Definition at line 168 of file sf_psi.hpp.

◆ psi_1_e()

int gsl::sf::psi_1_e	(	double const	x,
		result &	result
	)

inline

C++ version of gsl_sf_psi_1_e().

Poly-Gamma Functions

psi(m,x) := (d/dx)^m psi(0,x) = (d/dx)^{m+1} log(gamma(x))

Tri-Gamma Function psi^(1)(n)

n > 0

Parameters

x	A real value
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS or GSL_EDOM

Definition at line 155 of file sf_psi.hpp.

◆ psi_1_int()

double gsl::sf::psi_1_int ( int const n )

inline

C++ version of gsl_sf_psi_1_int().

Poly-Gamma Functions

psi(m,x) := (d/dx)^m psi(0,x) = (d/dx)^{m+1} log(gamma(x))

Di-Gamma Function psi(z) for general complex argument z = x + iy

Parameters

n	An integer

Returns: The function value

Definition at line 141 of file sf_psi.hpp.

References gsl::rstat::n().

◆ psi_1_int_e()

int gsl::sf::psi_1_int_e	(	int const	n,
		result &	result
	)

inline

C++ version of gsl_sf_psi_1_int_e().

Poly-Gamma Functions

psi(m,x) := (d/dx)^m psi(0,x) = (d/dx)^{m+1} log(gamma(x))

Di-Gamma Function psi(z) for general complex argument z = x + iy

Parameters

n	An integer
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS or GSL_EDOM

Definition at line 130 of file sf_psi.hpp.

References gsl::rstat::n().

◆ psi_1piy()

double gsl::sf::psi_1piy ( double const y )

inline

C++ version of gsl_sf_psi_1piy().

Poly-Gamma Functions

psi(m,x) := (d/dx)^m psi(0,x) = (d/dx)^{m+1} log(gamma(x))

Di-Gamma Function Re[psi(1 + I y)]

Parameters

y	The imaginary part

Returns: The function value

Definition at line 105 of file sf_psi.hpp.

◆ psi_1piy_e()

int gsl::sf::psi_1piy_e	(	double const	y,
		result &	result
	)

inline

C++ version of gsl_sf_psi_1piy_e().

Poly-Gamma Functions

psi(m,x) := (d/dx)^m psi(0,x) = (d/dx)^{m+1} log(gamma(x))

Di-Gamma Function Re[psi(1 + I y)]

Parameters

y	The imaginary part
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS

Definition at line 94 of file sf_psi.hpp.

◆ psi_e()

int gsl::sf::psi_e	(	double const	x,
		result &	result
	)

inline

C++ version of gsl_sf_psi_e().

Poly-Gamma Functions

psi(m,x) := (d/dx)^m psi(0,x) = (d/dx)^{m+1} log(gamma(x))

Di-Gamma Function psi(x) = psi(0, x)

x != 0.0, -1.0, -2.0, ...

Parameters

x	A real value
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS or GSL_EDOM or GSL_ELOSS

Definition at line 69 of file sf_psi.hpp.

◆ psi_int()

double gsl::sf::psi_int ( int const n )

inline

C++ version of gsl_sf_psi_int().

Poly-Gamma Functions

psi(m,x) := (d/dx)^m psi(0,x) = (d/dx)^{m+1} log(gamma(x))

Di-Gamma Function psi(n) = psi(0,n)

n > 0

Parameters

n	An integer

Returns: The function value

Definition at line 55 of file sf_psi.hpp.

References gsl::rstat::n().

◆ psi_int_e()

int gsl::sf::psi_int_e	(	int const	n,
		result &	result
	)

inline

C++ version of gsl_sf_psi_int_e().

Poly-Gamma Functions

psi(m,x) := (d/dx)^m psi(0,x) = (d/dx)^{m+1} log(gamma(x))

Di-Gamma Function psi(n) = psi(0,n)

n > 0

Parameters

n	An integer
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS or GSL_EDOM

Definition at line 42 of file sf_psi.hpp.

References gsl::rstat::n().

◆ psi_n()

double gsl::sf::psi_n	(	int const	n,
		double const	x
	)

inline

C++ version of gsl_sf_psi_n().

Poly-Gamma Functions

psi(m,x) := (d/dx)^m psi(0,x) = (d/dx)^{m+1} log(gamma(x))

Poly-Gamma Function psi^(n)(x)

n >= 0, x > 0.0

Parameters

n	An integer
x	A real value

Returns: The function value

Definition at line 197 of file sf_psi.hpp.

References gsl::rstat::n().

◆ psi_n_e()

int gsl::sf::psi_n_e	(	int const	n,
		double const	x,
		result &	result
	)

inline

C++ version of gsl_sf_psi_n_e().

Poly-Gamma Functions

psi(m,x) := (d/dx)^m psi(0,x) = (d/dx)^{m+1} log(gamma(x))

Poly-Gamma Function psi^(n)(x)

n >= 0, x > 0.0

Parameters

n	An integer
x	A real value
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS or GSL_EDOM

Definition at line 183 of file sf_psi.hpp.

References gsl::rstat::n().

◆ rect_to_polar()

int gsl::sf::rect_to_polar	(	double const	x,
		double const	y,
		result &	r,
		result &	theta
	)

inline

C++ version of gsl_sf_rect_to_polar().

Parameters

x	A real value
y	A real value
r	The distance as a `gsl::sf::result` object
theta	The angle as a `gsl::sf::result` object

Returns: GSL_SUCCESS or GSL_ELOSS

Definition at line 164 of file sf_trig.hpp.

◆ result_smash_e()

int gsl::sf::result_smash_e	(	gsl_sf_result_e10 const &	re,
		gsl_sf_result &	r
	)

inline

C++ version of gsl_sf_result_smash_e().

Parameters

re	Object of type result_e10
r	Object of type result

Returns: Error code

Definition at line 41 of file sf_result.hpp.

◆ Shi()

double gsl::sf::Shi ( double const x )

inline

C++ version of gsl_sf_Shi().

Shi(x) := Integrate[ Sinh[t]/t, {t,0,x}]

Parameters

x	A real number

Returns: The function value

Definition at line 209 of file sf_expint.hpp.

◆ Shi_e()

int gsl::sf::Shi_e	(	double const	x,
		result &	result
	)

inline

C++ version of gsl_sf_Shi_e().

Shi(x) := Integrate[ Sinh[t]/t, {t,0,x}]

Parameters

x	A real number
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS or GSL_EDOM or GSL_EOVRFLW or GSL_EUNDRFLW

Definition at line 202 of file sf_expint.hpp.

◆ Si()

double gsl::sf::Si ( double const x )

inline

C++ version of gsl_sf_Si().

Si(x) := Integrate[ Sin[t]/t, {t,0,x}]

Parameters

x	A real number

Returns: The function value

Definition at line 262 of file sf_expint.hpp.

◆ Si_e()

int gsl::sf::Si_e	(	double const	x,
		result &	result
	)

inline

C++ version of gsl_sf_Si_e().

Si(x) := Integrate[ Sin[t]/t, {t,0,x}]

Parameters

x	A real number
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS

Definition at line 255 of file sf_expint.hpp.

◆ sin()

double gsl::sf::sin ( double const x )

inline

C++ version of gsl_sf_sin().

Parameters

x	A real value

Returns: The function value

Definition at line 41 of file sf_trig.hpp.

◆ sin_e()

int gsl::sf::sin_e	(	double	x,
		result &	result
	)

inline

C++ version of gsl_sf_sin_e().

Parameters

x	A real value
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS

Definition at line 35 of file sf_trig.hpp.

◆ sin_err_e()

int gsl::sf::sin_err_e	(	double const	x,
		double const	dx,
		result &	result
	)

inline

C++ version of gsl_sf_sin_err_e().

Sin(x) for quantity with an associated error.

Parameters

x	A real value
dx	The error in `x`
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS or GSL_EDOM

Definition at line 174 of file sf_trig.hpp.

◆ sin_pi()

double gsl::sf::sin_pi ( double const x )

inline

C++ version of gsl_sf_sin_pi().

Sine function

Parameters

x	A real number

Returns: The function value

Definition at line 43 of file sf_sincos_pi.hpp.

◆ sin_pi_e()

int gsl::sf::sin_pi_e	(	double	x,
		result &	result
	)

inline

C++ version of gsl_sf_sin_pi_e().

Sine function

Parameters

x	A real number
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS or GSL_EOVRFLW or GSL_EUNDRFLW

Definition at line 36 of file sf_sincos_pi.hpp.

◆ sinc()

double gsl::sf::sinc ( double const x )

inline

C++ version of gsl_sf_sinc().

Sinc(x) = sin(pi x) / (pi x)

Parameters

x	A real value

Returns: The function value

Definition at line 115 of file sf_trig.hpp.

◆ sinc_e()

int gsl::sf::sinc_e	(	double	x,
		result &	result
	)

inline

C++ version of gsl_sf_sinc_e().

Sinc(x) = sin(pi x) / (pi x)

Parameters

x	A real value
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS

Definition at line 108 of file sf_trig.hpp.

◆ synchrotron_1()

double gsl::sf::synchrotron_1 ( double const x )

inline

C++ version of gsl_sf_synchrotron_1().

First synchrotron function: synchrotron_1(x) = x Integral[ K_{5/3}(t), {t, x, Infinity}]

Parameters

x	A real value

Returns: The function value

Definition at line 46 of file sf_synchrotron.hpp.

◆ synchrotron_1_e()

int gsl::sf::synchrotron_1_e	(	double const	x,
		result &	result
	)

inline

C++ version of gsl_sf_synchrotron_1_e().

First synchrotron function: synchrotron_1(x) = x Integral[ K_{5/3}(t), {t, x, Infinity}]

Parameters

x	A real value
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS or GSL_EDOM or GSL_EUNDRFLW

Definition at line 37 of file sf_synchrotron.hpp.

◆ synchrotron_2()

double gsl::sf::synchrotron_2 ( double const x )

inline

C++ version of gsl_sf_synchrotron_2().

Second synchroton function: synchrotron_2(x) = x * K_{2/3}(x)

Parameters

x	A real value

Returns: The function value

Definition at line 64 of file sf_synchrotron.hpp.

◆ synchrotron_2_e()

int gsl::sf::synchrotron_2_e	(	double const	x,
		result &	result
	)

inline

C++ version of gsl_sf_synchrotron_2_e().

Second synchroton function: synchrotron_2(x) = x * K_{2/3}(x)

Parameters

x	A real value
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS or GSL_EDOM or GSL_EUNDRFLW

Definition at line 55 of file sf_synchrotron.hpp.

◆ taylorcoeff()

double gsl::sf::taylorcoeff	(	int const	n,
		double const	x
	)

inline

C++ version of gsl_sf_taylorcoeff().

x^n / n!

x >= 0.0, n >= 0

Parameters

n	An integer
x	A real number

Returns: The function value

Definition at line 174 of file sf_gamma.hpp.

References gsl::rstat::n().

◆ taylorcoeff_e()

int gsl::sf::taylorcoeff_e	(	int const	n,
		double const	x,
		result &	result
	)

inline

C++ version of gsl_sf_taylorcoeff_e().

x^n / n!

x >= 0.0, n >= 0

Parameters

n	An integer
x	A real number
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS or GSL_EDOM or GSL_EOVRFLW or GSL_EUNDRFLW

Definition at line 163 of file sf_gamma.hpp.

References gsl::rstat::n().

◆ transport_2()

double gsl::sf::transport_2 ( double const x )

inline

C++ version of gsl_sf_transport_2().

Transport function: J(2,x) := Integral[ t^2 e^t /(e^t - 1)^2, {t,0,x}]

Parameters

x	A real value

Returns: The function value

Definition at line 46 of file sf_transport.hpp.

◆ transport_2_e()

int gsl::sf::transport_2_e	(	double const	x,
		result &	result
	)

inline

C++ version of gsl_sf_transport_2_e().

Transport function: J(2,x) := Integral[ t^2 e^t /(e^t - 1)^2, {t,0,x}]

Parameters

x	A real value
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS or GSL_EDOM

Definition at line 37 of file sf_transport.hpp.

◆ transport_3()

double gsl::sf::transport_3 ( double const x )

inline

C++ version of gsl_sf_transport_3().

Transport function: J(3,x) := Integral[ t^3 e^t /(e^t - 1)^2, {t,0,x}]

Parameters

x	A real value

Returns: The function value

Definition at line 64 of file sf_transport.hpp.

◆ transport_3_e()

int gsl::sf::transport_3_e	(	double const	x,
		result &	result
	)

inline

C++ version of gsl_sf_transport_3_e().

Transport function: J(3,x) := Integral[ t^3 e^t /(e^t - 1)^2, {t,0,x}]

Parameters

x	A real value
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS or GSL_EDOM or GSL_EUNDRFLW

Definition at line 55 of file sf_transport.hpp.

◆ transport_4()

double gsl::sf::transport_4 ( double const x )

inline

C++ version of gsl_sf_transport_4().

Transport function: J(4,x) := Integral[ t^4 e^t /(e^t - 1)^2, {t,0,x}]

Parameters

x	A real value

Returns: The function value

Definition at line 82 of file sf_transport.hpp.

◆ transport_4_e()

int gsl::sf::transport_4_e	(	double const	x,
		result &	result
	)

inline

C++ version of gsl_sf_transport_4_e().

Transport function: J(4,x) := Integral[ t^4 e^t /(e^t - 1)^2, {t,0,x}]

Parameters

x	A real value
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS or GSL_EDOM or GSL_EUNDRFLW

Definition at line 73 of file sf_transport.hpp.

◆ transport_5()

double gsl::sf::transport_5 ( double const x )

inline

C++ version of gsl_sf_transport_5().

Transport function: J(5,x) := Integral[ t^5 e^t /(e^t - 1)^2, {t,0,x}]

Parameters

x	A real value

Returns: The function value

Definition at line 100 of file sf_transport.hpp.

◆ transport_5_e()

int gsl::sf::transport_5_e	(	double const	x,
		result &	result
	)

inline

C++ version of gsl_sf_transport_5_e().

Transport function: J(5,x) := Integral[ t^5 e^t /(e^t - 1)^2, {t,0,x}]

Parameters

x	A real value
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS or GSL_EDOM or GSL_EUNDRFLW

Definition at line 91 of file sf_transport.hpp.

◆ zeta()

double gsl::sf::zeta ( double const s )

inline

C++ version of gsl_sf_zeta().

Riemann Zeta Function zeta(x) = Sum[ k^(-s), {k,1,Infinity} ], s != 1.0

s != 1.0

Parameters

s	A real value

Returns: The function value

Definition at line 72 of file sf_zeta.hpp.

Referenced by gsl::ran::lognormal(), gsl::cdf::lognormal_P(), gsl::ran::lognormal_pdf(), gsl::cdf::lognormal_Pinv(), gsl::cdf::lognormal_Q(), and gsl::cdf::lognormal_Qinv().

◆ zeta_e()

int gsl::sf::zeta_e	(	double const	s,
		result &	result
	)

inline

C++ version of gsl_sf_zeta_e().

Riemann Zeta Function zeta(x) = Sum[ k^(-s), {k,1,Infinity} ], s != 1.0

s != 1.0

Parameters

s	A real value
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS or GSL_EDOM or GSL_EOVRFLW

Definition at line 61 of file sf_zeta.hpp.

◆ zeta_int()

double gsl::sf::zeta_int ( int const n )

inline

C++ version of gsl_sf_zeta_int().

Riemann Zeta Function zeta(n) = Sum[ k^(-n), {k,1,Infinity} ]

n=integer, n != 1

Parameters

n	An integer

Returns: The function value

Definition at line 50 of file sf_zeta.hpp.

References gsl::rstat::n().

◆ zeta_int_e()

int gsl::sf::zeta_int_e	(	int const	n,
		result &	result
	)

inline

C++ version of gsl_sf_zeta_int_e().

Riemann Zeta Function zeta(n) = Sum[ k^(-n), {k,1,Infinity} ]

n=integer, n != 1

Parameters

n	An integer
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS or GSL_EDOM or GSL_EOVRFLW

Definition at line 39 of file sf_zeta.hpp.

References gsl::rstat::n().

◆ zetam1()

double gsl::sf::zetam1 ( double const s )

inline

C++ version of gsl_sf_zetam1().

Riemann Zeta Function minus 1 useful for evaluating the fractional part of Riemann zeta for large argument

s != 1.0

Parameters

s	A real value

Returns: The function value

Definition at line 96 of file sf_zeta.hpp.

◆ zetam1_e()

int gsl::sf::zetam1_e	(	double const	s,
		result &	result
	)

inline

C++ version of gsl_sf_zetam1_e().

Riemann Zeta Function minus 1 useful for evaluating the fractional part of Riemann zeta for large argument

s != 1.0

Parameters

s	A real value
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS or GSL_EDOM or GSL_EOVRFLW

Definition at line 84 of file sf_zeta.hpp.

◆ zetam1_int()

double gsl::sf::zetam1_int ( int const s )

inline

C++ version of gsl_sf_zetam1_int().

Riemann Zeta Function minus 1 for integer arg useful for evaluating the fractional part of Riemann zeta for large argument

s != 1.0

Parameters

s	A real value

Returns: The function value

Definition at line 120 of file sf_zeta.hpp.

◆ zetam1_int_e()

int gsl::sf::zetam1_int_e	(	int const	s,
		result &	result
	)

inline

C++ version of gsl_sf_zetam1_int_e().

Riemann Zeta Function minus 1 for integer arg useful for evaluating the fractional part of Riemann zeta for large argument

s != 1.0

Parameters

s	A real value
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS or GSL_EDOM or GSL_EOVRFLW

Definition at line 108 of file sf_zeta.hpp.

Variable Documentation

◆ DOUBLEFACT_NMAX

double const gsl::sf::DOUBLEFACT_NMAX = GSL_SF_DOUBLEFACT_NMAX

The maximum n such that doublefact(n) does not give an overflow.

Definition at line 592 of file sf_gamma.hpp.

◆ FACT_NMAX

double const gsl::sf::FACT_NMAX = GSL_SF_FACT_NMAX

The maximum n such that fact(n) does not give an overflow.

Definition at line 588 of file sf_gamma.hpp.

◆ GAMMA_XMAX

double const gsl::sf::GAMMA_XMAX = GSL_SF_GAMMA_XMAX

The maximum x such that gamma(x) is not considered an overflow.

Definition at line 584 of file sf_gamma.hpp.

Namespaces

Typedefs

Functions

Variables

Detailed Description

Typedef Documentation

◆ result

◆ result_e10

Function Documentation

◆ angle_restrict_pos()

◆ angle_restrict_pos_e()

◆ angle_restrict_pos_err_e()

◆ angle_restrict_symm()

◆ angle_restrict_symm_e()

◆ angle_restrict_symm_err_e()

◆ atanint()

◆ atanint_e()

◆ beta()

◆ beta_e()

◆ beta_inc()

◆ beta_inc_e()

◆ Chi()

◆ Chi_e()

◆ choose()

◆ choose_e()

◆ Ci()

◆ Ci_e()

◆ clausen()

◆ clausen_e()

◆ complex_cos_e()

◆ complex_dilog_e()

◆ complex_dilog_xy_e()

◆ complex_log_e()

◆ complex_logsin_e()

◆ complex_psi_e()

◆ complex_sin_e()

◆ complex_spence_xy_e()

◆ conicalP_0()

◆ conicalP_0_e()

◆ conicalP_1()

◆ conicalP_1_e()

◆ conicalP_cyl_reg()

◆ conicalP_cyl_reg_e()

◆ conicalP_half()

◆ conicalP_half_e()

◆ conicalP_mhalf()

◆ conicalP_mhalf_e()

◆ conicalP_sph_reg()

◆ conicalP_sph_reg_e()

◆ cos()

◆ cos_e()

◆ cos_err_e()

◆ cos_pi()

◆ cos_pi_e()

◆ coupling_3j()

◆ coupling_3j_e()

◆ coupling_6j()

◆ coupling_6j_e()

◆ coupling_9j()

◆ coupling_9j_e()

◆ coupling_RacahW()

◆ coupling_RacahW_e()

◆ dawson()

◆ dawson_e()

◆ debye_1()

◆ debye_1_e()

◆ debye_2()

◆ debye_2_e()

◆ debye_3()

◆ debye_3_e()

◆ debye_4()

◆ debye_4_e()

◆ debye_5()

◆ debye_5_e()

◆ debye_6()

◆ debye_6_e()

◆ dilog()

◆ dilog_e()

◆ doublefact()

◆ doublefact_e()