ccgsl  1.16.1
gsl::sf Namespace Reference

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

Namespaces

 airy
 Namespace for Airy functions.
 
 bessel
 Namespace for Bessel functions.
 
 coulomb
 Namespace for gsl_sf_coulomb functions.
 
 ellint
 Namespace for elliptic integrals.
 
 lambert
 Lambert functions.
 
 legendre
 Legendre functions.
 
 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 gsl_sf_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...
 
int gegenpoly_array (int nmax, double lambda, double x, double *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 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

typedef gsl_sf_result gsl::sf::result

Typedef for gsl_sf_result.

Definition at line 30 of file sf_result.hpp.

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

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
thetaA real value (angle)
Returns
The function value

Definition at line 216 of file sf_trig.hpp.

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
thetaA real value (angle)
Returns
GSL_SUCCESS or GSL_ELOSS

Definition at line 208 of file sf_trig.hpp.

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
thetaA real value (angle)
resultThe result as a gsl::sf::result object
Returns
Error code on failure

Definition at line 232 of file sf_trig.hpp.

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
thetaA real value (angle)
Returns
The function value

Definition at line 200 of file sf_trig.hpp.

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
thetaA real value (angle)
Returns
GSL_SUCCESS or GSL_ELOSS

Definition at line 192 of file sf_trig.hpp.

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
thetaA real value (angle)
resultThe result as a gsl::sf::result object
Returns
Error code on failure

Definition at line 224 of file sf_trig.hpp.

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

C++ version of gsl_sf_atanint().

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

Parameters
xA real number
Returns
The function value

Definition at line 296 of file sf_expint.hpp.

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
xA real number
resultThe result as a gsl::sf::result object
Returns
Error code on failure

Definition at line 289 of file sf_expint.hpp.

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
aA real number
bA real number
Returns
The function value

Definition at line 504 of file sf_gamma.hpp.

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
aA real number
bA real number
resultThe result as a gsl::sf::result object
Returns
GSL_SUCCESS or GSL_EOVRFLW or GSL_EUNDRFLW or GSL_EDOM

Definition at line 492 of file sf_gamma.hpp.

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
aA real number
bA real number
xA real number
Returns
The function value

Definition at line 530 of file sf_gamma.hpp.

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
aA real number
bA real number
xA real number
resultThe result as a gsl::sf::result object
Returns
GSL_SUCCESS or GSL_EDOM or GSL_EUNDRFLW

Definition at line 517 of file sf_gamma.hpp.

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
xA real number
Returns
The function value

Definition at line 228 of file sf_expint.hpp.

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
xA real number
resultThe 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.

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

C++ version of gsl_sf_choose().

n choose m

Parameters
nAn integer
mAn integer
Returns
The function value

Definition at line 265 of file sf_gamma.hpp.

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
nAn integer
mAn integer
resultThe result as a gsl::sf::result object
Returns
GSL_SUCCESS or GSL_EDOM or GSL_EOVRFLW

Definition at line 256 of file sf_gamma.hpp.

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
xA real number
Returns
The function value

Definition at line 281 of file sf_expint.hpp.

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
xA real number
resultThe result as a gsl::sf::result object
Returns
GSL_SUCCESS or GSL_EDOM

Definition at line 272 of file sf_expint.hpp.

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
xA real value
Returns
The function applied to x

Definition at line 52 of file sf_clausen.hpp.

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
xA real value
resultThe result as a gsl::sf::result object
Returns
Error code on failure

Definition at line 40 of file sf_clausen.hpp.

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
zrReal part of a complex number
ziImaginary part of a complex number
czrThe real part of the result as a gsl::sf::result object
cziThe 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.

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
rA real number
thetaA real number
result_reReal part of result as gsl::sf::result object
result_imImaginary part of result as gsl::sf::result object
Returns
Error code on failure

Definition at line 73 of file sf_dilog.hpp.

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
xA real number
yA real number
result_reReal part of result as gsl::sf::result object
result_imImaginary part of result as gsl::sf::result object
Returns
Error code on failure

Definition at line 60 of file sf_dilog.hpp.

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
zrReal part of a complex number
ziImaginary part of a complex number
lnrThe result (ln r) as a gsl::sf::result object
thetaThe result (theta) as a gsl::sf::result object
Returns
GSL_SUCCESS or GSL_EDOM

Definition at line 69 of file sf_log.hpp.

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
zrReal part of a complex number
ziImaginary part of a complex number
lszrThe real part of the result as a gsl::sf::result object
lsziThe 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.

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
xReal part of complex number
yImaginary part of complex number
result_reReal part of result as gsl::sf::result object
result_imImaginary part of result as gsl::sf::result object
Returns
GSL_SUCCESS

Definition at line 117 of file sf_psi.hpp.

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
zrReal part of a complex number
ziImaginary part of a complex number
szrThe real part of the result as a gsl::sf::result object
sziThe 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.

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
xA real number
yA real number
real_spReal part of result as gsl::sf::result object
imag_spImaginary part of result as gsl::sf::result object
Returns
Error code on failure

Definition at line 84 of file sf_dilog.hpp.

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
lambdaA real value
xA real value
Returns
The function value

Definition at line 394 of file sf_legendre.hpp.

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
lambdaA real value
xA real value
resultThe result as a gsl::sf::result object
Returns
GSL_SUCCESS or GSL_EDOM

Definition at line 382 of file sf_legendre.hpp.

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
lambdaA real value
xA real value
Returns
The function value

Definition at line 419 of file sf_legendre.hpp.

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
lambdaA real value
xA real value
resultThe result as a gsl::sf::result object
Returns
GSL_SUCCESS or GSL_EDOM

Definition at line 407 of file sf_legendre.hpp.

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
mAn integer
lambdaA real value
xA real value
Returns
The function value

Definition at line 473 of file sf_legendre.hpp.

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
mAn integer
lambdaA real value
xA real value
resultThe result as a gsl::sf::result object
Returns
GSL_SUCCESS or GSL_EDOM

Definition at line 460 of file sf_legendre.hpp.

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
lambdaA real value
xA real value
Returns
The function value

Definition at line 344 of file sf_legendre.hpp.

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

Definition at line 332 of file sf_legendre.hpp.

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
lambdaA real value
xA real value
Returns
The function value

Definition at line 369 of file sf_legendre.hpp.

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
lambdaA real value
xA real value
resultThe result as a gsl::sf::result object
Returns
GSL_SUCCESS or GSL_EDOM

Definition at line 357 of file sf_legendre.hpp.

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
lAn integer
lambdaA real value
xA real value
Returns
The function value

Definition at line 446 of file sf_legendre.hpp.

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
lAn integer
lambdaA real value
xA real value
resultThe result as a gsl::sf::result object
Returns
GSL_SUCCESS or GSL_EDOM

Definition at line 433 of file sf_legendre.hpp.

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

C++ version of gsl_sf_cos().

Parameters
xA real value
Returns
The function value

Definition at line 54 of file sf_trig.hpp.

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

C++ version of gsl_sf_cos_e().

Parameters
xA real value
resultThe result as a gsl::sf::result object
Returns
GSL_SUCCESS

Definition at line 48 of file sf_trig.hpp.

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
xA real value
dxThe error in x
resultThe result as a gsl::sf::result object
Returns
GSL_SUCCESS

Definition at line 184 of file sf_trig.hpp.

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_jaCoupling coefficient in half-integer units
two_jbCoupling coefficient in half-integer units
two_jcCoupling coefficient in half-integer units
two_maCoupling coefficient in half-integer units
two_mbCoupling coefficient in half-integer units
two_mcCoupling coefficient in half-integer units
Returns
The Wigner 3-j coefficient

Definition at line 53 of file sf_coupling.hpp.

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_jaCoupling coefficient in half-integer units
two_jbCoupling coefficient in half-integer units
two_jcCoupling coefficient in half-integer units
two_maCoupling coefficient in half-integer units
two_mbCoupling coefficient in half-integer units
two_mcCoupling coefficient in half-integer units
resultThe 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.

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_jaCoupling coefficient in half-integer units
two_jbCoupling coefficient in half-integer units
two_jcCoupling coefficient in half-integer units
two_jdCoupling coefficient in half-integer units
two_jeCoupling coefficient in half-integer units
two_jfCoupling coefficient in half-integer units
Returns
The Wigner 6-j coefficient

Definition at line 79 of file sf_coupling.hpp.

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_jaCoupling coefficient in half-integer units
two_jbCoupling coefficient in half-integer units
two_jcCoupling coefficient in half-integer units
two_jdCoupling coefficient in half-integer units
two_jeCoupling coefficient in half-integer units
two_jfCoupling coefficient in half-integer units
resultCoupling coefficient in half-integer units
Returns
GSL_SUCCESS or GSL_EDOM or GSL_EOVERFLW

Definition at line 66 of file sf_coupling.hpp.

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_jaCoupling coefficient in half-integer units
two_jbCoupling coefficient in half-integer units
two_jcCoupling coefficient in half-integer units
two_jdCoupling coefficient in half-integer units
two_jeCoupling coefficient in half-integer units
two_jfCoupling coefficient in half-integer units
two_jgCoupling coefficient in half-integer units
two_jhCoupling coefficient in half-integer units
two_jiCoupling coefficient in half-integer units
Returns
The Wigner 9-j coefficient

Definition at line 138 of file sf_coupling.hpp.

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_jaCoupling coefficient in half-integer units
two_jbCoupling coefficient in half-integer units
two_jcCoupling coefficient in half-integer units
two_jdCoupling coefficient in half-integer units
two_jeCoupling coefficient in half-integer units
two_jfCoupling coefficient in half-integer units
two_jgCoupling coefficient in half-integer units
two_jhCoupling coefficient in half-integer units
two_jiCoupling coefficient in half-integer units
resultThe 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.

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_jaCoupling coefficient in half-integer units
two_jbCoupling coefficient in half-integer units
two_jcCoupling coefficient in half-integer units
two_jdCoupling coefficient in half-integer units
two_jeCoupling coefficient in half-integer units
two_jfCoupling coefficient in half-integer units
Returns
The function value

Definition at line 105 of file sf_coupling.hpp.

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_jaCoupling coefficient in half-integer units
two_jbCoupling coefficient in half-integer units
two_jcCoupling coefficient in half-integer units
two_jdCoupling coefficient in half-integer units
two_jeCoupling coefficient in half-integer units
two_jfCoupling coefficient in half-integer units
resultThe 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.

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
xA real number
Returns
The integral

Definition at line 47 of file sf_dawson.hpp.

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
xA real number
resultThe result as a gsl::sf::result object
Returns
Error code on failure

Definition at line 38 of file sf_dawson.hpp.

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
xA real number
Returns
The function value

Definition at line 43 of file sf_debye.hpp.

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
xA real number
resultThe result as a gsl::sf::result object
Returns
Error code on failure

Definition at line 36 of file sf_debye.hpp.

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
xA real number
Returns
The function value

Definition at line 58 of file sf_debye.hpp.

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
xA real number
resultThe result as a gsl::sf::result object
Returns
GSL_SUCCESS or GSL_EDOM

Definition at line 51 of file sf_debye.hpp.

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
xA real number
Returns
The function value

Definition at line 73 of file sf_debye.hpp.

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
xA real number
resultThe 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.

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
xA real number
Returns
The function value

Definition at line 88 of file sf_debye.hpp.

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
xA real number
resultThe 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.

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
xA real number
Returns
The function value

Definition at line 103 of file sf_debye.hpp.

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
xA real number
resultThe 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.

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
xA real number
Returns
The function value

Definition at line 118 of file sf_debye.hpp.

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
xA real number
resultThe 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.

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
xA real number
Returns
Error code on failure

Definition at line 49 of file sf_dilog.hpp.

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
xA real number
resultThe result as a gsl::sf::result object
Returns
Error code on failure

Definition at line 39 of file sf_dilog.hpp.

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

C++ version of gsl_sf_doublefact().

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

Parameters
nAn integer
Returns
The function value

Definition at line 193 of file sf_gamma.hpp.

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
nAn integer
resultThe result as a gsl::sf::result object
Returns
GSL_SUCCESS or GSL_EDOM or GSL_EOVRFLW

Definition at line 185 of file sf_gamma.hpp.

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
xA real number
Returns
The function value

Definition at line 77 of file sf_erf.hpp.

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
xA real number
resultThe result as a gsl::sf::result object
Returns
GSL_SUCCESS

Definition at line 69 of file sf_erf.hpp.

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
xA real number
Returns
The function value

Definition at line 111 of file sf_erf.hpp.

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
xA real number
resultThe result as a gsl::sf::result object
Returns
GSL_SUCCESS

Definition at line 95 of file sf_erf.hpp.

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
xA real number
Returns
The function value

Definition at line 103 of file sf_erf.hpp.

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
xA real number
resultThe result as a gsl::sf::result object
Returns
GSL_SUCCESS

Definition at line 86 of file sf_erf.hpp.

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
xA real number
Returns
The function value

Definition at line 45 of file sf_erf.hpp.

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
xA real number
resultThe result as a gsl::sf::result object
Returns
GSL_SUCCESS

Definition at line 37 of file sf_erf.hpp.

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
sA real value
Returns
The function value

Definition at line 181 of file sf_zeta.hpp.

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
sA real value
resultThe 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.

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
nAn integer
Returns
The function value

Definition at line 163 of file sf_zeta.hpp.

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
nAn integer
resultThe 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.

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

C++ version of gsl_sf_exp().

Exponential function

Parameters
xA real number
Returns
The function value

Definition at line 43 of file sf_exp.hpp.

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

C++ version of gsl_sf_exp_e().

Exponential function

Parameters
xA real number
resultThe 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.

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

C++ version of gsl_sf_exp_e10_e().

Exp(x)

Parameters
xA real number
resultThe 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.

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
xA real number
dxA real number
resultThe result as a gsl::sf::result object
Returns
Error code on failure

Definition at line 176 of file sf_exp.hpp.

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
xA real number
dxA real number
resultThe result as a gsl::sf::result object
Returns
Error code on failure

Definition at line 186 of file sf_exp.hpp.

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
xA real number
yA real number
Returns
The function value

Definition at line 70 of file sf_exp.hpp.

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
xA real number
yA real number
resultThe 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.

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
xA real number
yA real number
resultThe 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.

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
xA real number
dxA real number
yA real number
dyA real number
resultThe 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.

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
xA real number
dxA real number
yA real number
dyA real number
resultThe 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.

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
xA real number
Returns
The function value

Definition at line 247 of file sf_expint.hpp.

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
xA real number
resultThe result as a gsl::sf::result object
Returns
GSL_SUCCESS or GSL_EDOM

Definition at line 238 of file sf_expint.hpp.

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
xA real number
Returns
The function value

Definition at line 47 of file sf_expint.hpp.

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
xA real number
resultThe 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.

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
xA real number
Returns
The function value

Definition at line 108 of file sf_expint.hpp.

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
xA real number
resultThe 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.

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
xA real number
Returns
The function value

Definition at line 66 of file sf_expint.hpp.

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
xA real number
resultThe 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.

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
xA real number
Returns
GSL_SUCCESS or GSL_EDOM or GSL_EOVRFLW or GSL_EUNDRFLW

Definition at line 128 of file sf_expint.hpp.

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
xA real number
resultThe result as a gsl::sf::result object
Returns
The function value

Definition at line 118 of file sf_expint.hpp.

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
xA real number
Returns
GSL_SUCCESS or GSL_EDOM or GSL_EOVRFLW or GSL_EUNDRFLW

Definition at line 174 of file sf_expint.hpp.

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
xA real number
resultThe result as a gsl::sf::result object
Returns
The function value

Definition at line 163 of file sf_expint.hpp.

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
xA real number
Returns
The function value

Definition at line 194 of file sf_expint.hpp.

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
xA real number
resultThe 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.

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
nAn integer
xA real number
Returns
The function value

Definition at line 88 of file sf_expint.hpp.

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
nAn integer
xA real number
resultThe 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.

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
nAn integer
xA real number
Returns
GSL_SUCCESS or GSL_EDOM or GSL_EOVRFLW or GSL_EUNDRFLW

Definition at line 151 of file sf_expint.hpp.

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
nAn integer
xA real number
resultThe result as a gsl::sf::result object
Returns
The function value

Definition at line 140 of file sf_expint.hpp.

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

C++ version of gsl_sf_expm1().

exp(x)-1

Parameters
xA real number
Returns
The function value

Definition at line 97 of file sf_exp.hpp.

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

C++ version of gsl_sf_expm1_e().

exp(x)-1

Parameters
xA real number
resultThe result as a gsl::sf::result object
Returns
GSL_SUCCESS or GSL_EOVRFLW

Definition at line 89 of file sf_exp.hpp.

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
xA real number
Returns
The function value

Definition at line 113 of file sf_exp.hpp.

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
xA real number
Returns
The function value

Definition at line 129 of file sf_exp.hpp.

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
xA real number
resultThe result as a gsl::sf::result object
Returns
GSL_SUCCESS or GSL_EOVRFLW

Definition at line 121 of file sf_exp.hpp.

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
xA real number
resultThe result as a gsl::sf::result object
Returns
GSL_SUCCESS or GSL_EOVRFLW

Definition at line 105 of file sf_exp.hpp.

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
nA real number
xA real number
Returns
The function value

Definition at line 157 of file sf_exp.hpp.

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
nA real number
xA real number
resultThe result as a gsl::sf::result object
Returns
Error code on failure

Definition at line 166 of file sf_exp.hpp.

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
nA real number
xA real number
resultThe result as a gsl::sf::result object
Returns
Error code on failure

Definition at line 143 of file sf_exp.hpp.

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

C++ version of gsl_sf_fact().

n!

Parameters
nAn integer
Returns
The function value

Definition at line 177 of file sf_gamma.hpp.

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

C++ version of gsl_sf_fact_e().

n!

Parameters
nAn integer
resultThe result as a gsl::sf::result object
Returns
GSL_SUCCESS or GSL_EDOM or GSL_EOVRFLW

Definition at line 169 of file sf_gamma.hpp.

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
xA real number
Returns
The function value

Definition at line 61 of file sf_fermi_dirac.hpp.

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
xA real number
resultThe 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.

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
xA real number
Returns
The function value

Definition at line 78 of file sf_fermi_dirac.hpp.

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
xA real number
resultThe 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.

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
xA real number
Returns
The function value

Definition at line 95 of file sf_fermi_dirac.hpp.

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
xA real number
resultThe 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.

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
xA real number
Returns
The function value

Definition at line 165 of file sf_fermi_dirac.hpp.

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
xA real number
resultThe 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.

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
xA real number
Returns
The function value

Definition at line 148 of file sf_fermi_dirac.hpp.

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
xA real number
resultThe 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.

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
xA real number
bA real number
Returns
The function value

Definition at line 184 of file sf_fermi_dirac.hpp.

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
xA real number
bA real number
resultThe 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.

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
jAn integer
xA real number
Returns
The function value

Definition at line 114 of file sf_fermi_dirac.hpp.

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
jAn integer
xA real number
resultThe 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.

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
xA real number
Returns
The function value

Definition at line 44 of file sf_fermi_dirac.hpp.

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
xA real number
resultThe result as a gsl::sf::result object
Returns
GSL_SUCCESS or GSL_EUNDRFLW

Definition at line 36 of file sf_fermi_dirac.hpp.

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
xA real number
Returns
The function value

Definition at line 131 of file sf_fermi_dirac.hpp.

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
xA real number
resultThe 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.

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
xA real number
Returns
The function value

Definition at line 80 of file sf_gamma.hpp.

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
xA real number
resultThe result as a gsl::sf::result object
Returns
GSL_SUCCESS or GSL_EDOM or GSL_EOVRFLW or GSL_EROUND

Definition at line 71 of file sf_gamma.hpp.

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
aA real number
xA real number
Returns
The function value

Definition at line 440 of file sf_gamma.hpp.

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
aA real number
xA real number
resultThe result as a gsl::sf::result object
Returns
GSL_SUCCESS or GSL_EDOM

Definition at line 426 of file sf_gamma.hpp.

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
aA real number
xA real number
Returns
The function value

Definition at line 411 of file sf_gamma.hpp.

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
aA real number
xA real number
resultThe result as a gsl::sf::result object
Returns
GSL_SUCCESS or GSL_EDOM

Definition at line 398 of file sf_gamma.hpp.

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
aA real number
xA real number
Returns
The function value

Definition at line 384 of file sf_gamma.hpp.

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
aA real number
xA real number
resultThe result as a gsl::sf::result object
Returns
GSL_SUCCESS or GSL_EDOM

Definition at line 369 of file sf_gamma.hpp.

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

C++ version of gsl_sf_gammainv().

1/Gamma(x) Uses real Lanczos method.

Parameters
xA real number
Returns
The function value

Definition at line 118 of file sf_gamma.hpp.

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
xA real number
resultThe result as a gsl::sf::result object
Returns
GSL_SUCCESS or GSL_EUNDRFLW or GSL_EROUND

Definition at line 109 of file sf_gamma.hpp.

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
xA real number
Returns
The function value

Definition at line 100 of file sf_gamma.hpp.

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
xA real number
resultThe result as a gsl::sf::result object
Returns
GSL_SUCCESS or GSL_EDOM

Definition at line 90 of file sf_gamma.hpp.

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

C++ version of gsl_sf_gegenpoly_1().

Parameters
lambdaA real value greater than -0.5
xA real value
Returns
The function value

Definition at line 62 of file sf_gegenbauer.hpp.

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

C++ version of gsl_sf_gegenpoly_1_e().

Parameters
lambdaA real value greater than -0.5
xA real value
resultThe result as a gsl::sf::result object
Returns
GSL_SUCCESS

Definition at line 36 of file sf_gegenbauer.hpp.

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

C++ version of gsl_sf_gegenpoly_2().

Parameters
lambdaA real value greater than -0.5
xA real value
Returns
The function value

Definition at line 70 of file sf_gegenbauer.hpp.

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

C++ version of gsl_sf_gegenpoly_2_e().

Parameters
lambdaA real value greater than -0.5
xA real value
resultThe result as a gsl::sf::result object
Returns
GSL_SUCCESS

Definition at line 45 of file sf_gegenbauer.hpp.

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

C++ version of gsl_sf_gegenpoly_3().

Parameters
lambdaA real value greater than -0.5
xA real value
Returns
The function value

Definition at line 78 of file sf_gegenbauer.hpp.

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

C++ version of gsl_sf_gegenpoly_3_e().

Parameters
lambdaA real value greater than -0.5
xA real value
resultThe result as a gsl::sf::result object
Returns
GSL_SUCCESS

Definition at line 54 of file sf_gegenbauer.hpp.

int gsl::sf::gegenpoly_array ( int  nmax,
double  lambda,
double  x,
double *  result_array 
)
inline

C++ version of gsl_sf_gegenpoly_array().

Parameters
nmaxA nonnegative integer
lambdaA real value greater than -0.5
xA real value
result_arrayAn array of size nmax
Returns
GSL_SUCCESS or GSL_EDOM

Definition at line 107 of file sf_gegenbauer.hpp.

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

C++ version of gsl_sf_gegenpoly_n().

Parameters
nA nonnegative integer
lambdaA real value greater than -0.5
xA real value
Returns
The function value

Definition at line 97 of file sf_gegenbauer.hpp.

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

C++ version of gsl_sf_gegenpoly_n_e().

Parameters
nA nonnegative integer
lambdaA real value greater than -0.5
xA real value
resultThe result as a gsl::sf::result object
Returns
GSL_SUCCESS or GSL_EDOM

Definition at line 88 of file sf_gegenbauer.hpp.

int gsl::sf::gsl_sf_elljac_e ( double const  u,
double const  m,
double *  sn,
double *  cn,
double *  dn 
)

C++ version of gsl_sf_elljac_e().

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

Parameters
uA real number
mA real number
snA real number
cnA real number
dnA real number
Returns
GSL_SUCCESS or GSL_EDOM
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
xA real number
Returns
The function value

Definition at line 134 of file sf_erf.hpp.

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
xA real number
resultThe result as a gsl::sf::result object
Returns
GSL_SUCCESS or GSL_EUNDRFLW

Definition at line 123 of file sf_erf.hpp.

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
nAn integer
lAn integer
ZA real value
rA real value
Returns
The function value

Definition at line 73 of file sf_coulomb.hpp.

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
ZA real value
rA real value
Returns
The function value

Definition at line 48 of file sf_coulomb.hpp.

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
ZA real value
rA real value
resultThe result as a gsl::sf::result object
Returns
Error code on failure

Definition at line 38 of file sf_coulomb.hpp.

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
nAn integer
lan integer
ZA real value
rA real value
resultThe result as a gsl::sf::result object
Returns
Error code on failure

Definition at line 61 of file sf_coulomb.hpp.

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
cA real value
xA real value
Returns
The function value

Definition at line 52 of file sf_hyperg.hpp.

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
cA real value
xA real value
resultThe 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.

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
aA real value
bA real value
xA real value
Returns
The function value

Definition at line 98 of file sf_hyperg.hpp.

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
aA real value
bA real value
xA real value
resultThe result as a gsl::sf::result object
Returns
GSL_SUCCESS

Definition at line 87 of file sf_hyperg.hpp.

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
mAn integer
nAn integer
xA real value
Returns
The function value

Definition at line 75 of file sf_hyperg.hpp.

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
mAn integer
nAn integer
xA real value
resultThe result as a gsl::sf::result object
Returns
GSL_SUCCESS

Definition at line 64 of file sf_hyperg.hpp.

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
aA real value
bA real value
xA real value
Returns
The function value

Definition at line 298 of file sf_hyperg.hpp.

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
aA real value
bA real value
xA real value
resultThe result as a gsl::sf::result object
Returns
GSL_SUCCESS or GSL_EDOM

Definition at line 286 of file sf_hyperg.hpp.

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
aA real value
bA real value
cA real value
xA real value
Returns
The function value

Definition at line 193 of file sf_hyperg.hpp.

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
aRReal part of a complex number
aIImaginary part of a complex number
cA real value
xA real value
Returns
The function value

Definition at line 218 of file sf_hyperg.hpp.

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
aRReal part of a complex number
aIImaginary part of a complex number
cA real value
xA real value
resultThe result as a gsl::sf::result object
Returns
GSL_SUCCESS

Definition at line 206 of file sf_hyperg.hpp.

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
aRReal part of a complex number
aIImaginary part of a complex number
cA real value
xA real value
Returns
The function value

Definition at line 273 of file sf_hyperg.hpp.

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
aRReal part of a complex number
aIImaginary part of a complex number
cA real value
xA real value
resultThe result as a gsl::sf::result object
Returns
GSL_SUCCESS

Definition at line 259 of file sf_hyperg.hpp.

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
aA real value
bA real value
cA real value
xA real value
resultThe result as a gsl::sf::result object
Returns
GSL_SUCCESS

Definition at line 181 of file sf_hyperg.hpp.

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
aA real value
bA real value
cA real value
xA real value
Returns
The function value

Definition at line 245 of file sf_hyperg.hpp.

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
aA real value
bA real value
cA real value
xA real value
resultThe result as a gsl::sf::result object
Returns
GSL_SUCCESS

Definition at line 232 of file sf_hyperg.hpp.

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
aA real value
bA real value
xA real value
Returns
The function value

Definition at line 156 of file sf_hyperg.hpp.

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
aA real value
bA real value
xA real value
resultThe result as a gsl::sf::result object
Returns
GSL_SUCCESS

Definition at line 145 of file sf_hyperg.hpp.

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
aA real value
bA real value
xA real value
resultThe result as a gsl::sf::result object
Returns
GSL_SUCCESS

Definition at line 168 of file sf_hyperg.hpp.

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
mAn integer
nAn integer
xA real value
Returns
The function value

Definition at line 121 of file sf_hyperg.hpp.

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
mAn integer
nAn integer
xA real value
resultThe result as a gsl::sf::result object
Returns
GSL_SUCCESS

Definition at line 110 of file sf_hyperg.hpp.

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
mAn integer
nAn integer
xA real value
resultThe result as a gsl::sf::result object
Returns
GSL_SUCCESS

Definition at line 133 of file sf_hyperg.hpp.

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

C++ version of gsl_sf_hypot().

Parameters
xA real value
yA real value
Returns
The function value

Definition at line 70 of file sf_trig.hpp.

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

C++ version of gsl_sf_hypot_e().

Parameters
xA real value
yA real value
resultThe result as a gsl::sf::result object
Returns
GSL_SUCCESS

Definition at line 62 of file sf_trig.hpp.

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
sA real value
qA real value
Returns
The function value

Definition at line 144 of file sf_zeta.hpp.

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
sA real value
qA real value
resultThe 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.

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
aA real value
xA real value
Returns
The function value

Definition at line 66 of file sf_laguerre.hpp.

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
aA real value
xA real value
resultThe result as a gsl::sf::result object
Returns
GSL_SUCCESS

Definition at line 37 of file sf_laguerre.hpp.

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
aA real value
xA real value
Returns
The function value

Definition at line 74 of file sf_laguerre.hpp.

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
aA real value
xA real value
resultThe result as a gsl::sf::result object
Returns
GSL_SUCCESS

Definition at line 47 of file sf_laguerre.hpp.

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
aA real value
xA real value
Returns
The function value

Definition at line 82 of file sf_laguerre.hpp.

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
aA real value
xA real value
resultThe result as a gsl::sf::result object
Returns
GSL_SUCCESS

Definition at line 57 of file sf_laguerre.hpp.

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
nAn integer
aA real value
xA real value
Returns
The function value

Definition at line 108 of file sf_laguerre.hpp.

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
nAn integer
aA real value
xA real value
resultThe result as a gsl::sf::result object
Returns
GSL_SUCCESS or GSL_EDOM

Definition at line 95 of file sf_laguerre.hpp.

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
aA real number
bA real number
Returns
The function value

Definition at line 465 of file sf_gamma.hpp.

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
aA real number
bA real number
resultThe result as a gsl::sf::result object
Returns
GSL_SUCCESS or GSL_EDOM

Definition at line 453 of file sf_gamma.hpp.

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
xA real number
yA real number
resultThe result as a gsl::sf::result object
sgnRecord the sign here
Returns
GSL_SUCCESS or GSL_EDOM

Definition at line 479 of file sf_gamma.hpp.

double gsl::sf::lnchoose ( unsigned int  n,
unsigned int  m 
)
inline

C++ version of gsl_sf_lnchoose().

log(n choose m)

Parameters
nAn integer
mAn integer
Returns
The function value

Definition at line 246 of file sf_gamma.hpp.

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
nAn integer
mAn integer
resultThe result as a gsl::sf::result object
Returns
GSL_SUCCESS or GSL_EDOM

Definition at line 237 of file sf_gamma.hpp.

double gsl::sf::lncosh ( double const  x)
inline

C++ version of gsl_sf_lncosh().

Log(Cosh(x))

Parameters
xA real value
Returns
The function value

Definition at line 145 of file sf_trig.hpp.

int gsl::sf::lncosh_e ( double const  x,
result result 
)
inline

C++ version of gsl_sf_lncosh_e().

Log(Cosh(x))

Parameters
xA real value
resultThe result as a gsl::sf::result object
Returns
GSL_SUCCESS

Definition at line 138 of file sf_trig.hpp.

double gsl::sf::lndoublefact ( unsigned int const  n)
inline

C++ version of gsl_sf_lndoublefact().

log(n!!)

Parameters
nAn integer
Returns
The function value

Definition at line 227 of file sf_gamma.hpp.

int gsl::sf::lndoublefact_e ( unsigned int const  n,
result result 
)
inline

C++ version of gsl_sf_lndoublefact_e().

log(n!!)

Parameters
nAn integer
resultThe result as a gsl::sf::result object
Returns
GSL_SUCCESS

Definition at line 219 of file sf_gamma.hpp.

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
nAn integer
Returns
The function value

Definition at line 211 of file sf_gamma.hpp.

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
nAn integer
resultThe result as a gsl::sf::result object
Returns
GSL_SUCCESS

Definition at line 202 of file sf_gamma.hpp.

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
xA real number
Returns
The function value

Definition at line 50 of file sf_gamma.hpp.

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
zrThe real part
ziThe imaginary part
lnrResult as a gsl::sf::result object
argResult as a gsl::sf::result object
Returns
GSL_SUCCESS or GSL_EDOM or GSL_ELOSS

Definition at line 137 of file sf_gamma.hpp.

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
xA real number
resultThe 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.

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
xA real number
result_lgResult as a gsl::sf::result object
sgnThe sign as a return value
Returns
GSL_SUCCESS or GSL_EDOM or GSL_EROUND

Definition at line 61 of file sf_gamma.hpp.

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
aA real number
xA real number
Returns
The function value

Definition at line 291 of file sf_gamma.hpp.

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
aA real number
xA real number
resultThe result as a gsl::sf::result object
Returns
GSL_SUCCESS or GSL_EDOM

Definition at line 278 of file sf_gamma.hpp.

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
aA real number
xA real number
resultThe result as a gsl::sf::result object
sgnRecord the sign here
Returns
GSL_SUCCESS or GSL_EDOM

Definition at line 307 of file sf_gamma.hpp.

double gsl::sf::lnsinh ( double const  x)
inline

C++ version of gsl_sf_lnsinh().

Log(Sinh(x)), x > 0

Parameters
xA real value
Returns
The function value

Definition at line 130 of file sf_trig.hpp.

int gsl::sf::lnsinh_e ( double const  x,
result result 
)
inline

C++ version of gsl_sf_lnsinh_e().

Log(Sinh(x)), x > 0

Parameters
xA real value
resultThe result as a gsl::sf::result object
Returns
GSL_SUCCESS or GSL_EDOM

Definition at line 123 of file sf_trig.hpp.

double gsl::sf::log ( double const  x)
inline

C++ version of gsl_sf_log().

Parameters
xA real value
Returns
The function value

Definition at line 41 of file sf_log.hpp.

double gsl::sf::log_1plusx ( double const  x)
inline

C++ version of gsl_sf_log_1plusx().

Log(1 + x)

Parameters
xA real value
Returns
The function value

Definition at line 85 of file sf_log.hpp.

int gsl::sf::log_1plusx_e ( double const  x,
result result 
)
inline

C++ version of gsl_sf_log_1plusx_e().

Log(1 + x)

Parameters
xA real value
resultThe result as a gs::sf::result object
Returns
GSL_SUCCESS or GSL_EDOM

Definition at line 78 of file sf_log.hpp.

double gsl::sf::log_1plusx_mx ( double const  x)
inline

C++ version of gsl_sf_log_1plusx_mx().

Log(1 + x) - x

Parameters
xA real value
Returns
The function value

Definition at line 101 of file sf_log.hpp.

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
xA real value
resultThe result as a gs::sf::result object
Returns
GSL_SUCCESS or GSL_EDOM

Definition at line 93 of file sf_log.hpp.

double gsl::sf::log_abs ( double const  x)
inline

C++ version of gsl_sf_log_abs().

Log(|x|)

Parameters
xA real value
Returns
The function value

Definition at line 57 of file sf_log.hpp.

int gsl::sf::log_abs_e ( double const  x,
result result 
)
inline

C++ version of gsl_sf_log_abs_e().

Log(|x|)

Parameters
xA real value
resultThe result as a gs::sf::result object
Returns
GSL_SUCCESS or GSL_EDOM

Definition at line 49 of file sf_log.hpp.

int gsl::sf::log_e ( double const  x,
result result 
)
inline

C++ version of gsl_sf_log_e().

Parameters
xA real value
resultThe result as a gs::sf::result object
Returns
GSL_SUCCESS or GSL_EDOM

Definition at line 35 of file sf_log.hpp.

double gsl::sf::log_erfc ( double  x)
inline

C++ version of gsl_sf_log_erfc().

Log Complementary Error Function

Parameters
xA real number
Returns
The function value

Definition at line 60 of file sf_erf.hpp.

int gsl::sf::log_erfc_e ( double  x,
result result 
)
inline

C++ version of gsl_sf_log_erfc_e().

Log Complementary Error Function

Parameters
xA real number
resultThe result as a gsl::sf::result object
Returns
GSL_SUCCESS

Definition at line 53 of file sf_erf.hpp.

double gsl::sf::multiply ( double const  x,
double const  y 
)
inline

C++ version of gsl_sf_multiply().

Parameters
xA real number
yAnother real number
Returns
GSL_SUCCESS or GSL_EOVRFLW or GSL_EUNDRFLW

Definition at line 44 of file sf_elementary.hpp.

int gsl::sf::multiply_e ( double const  x,
double const  y,
result result 
)
inline

C++ version of gsl_sf_multiply_e().

Parameters
xA real number
yAnother real number
resultThe 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.

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
xA real number
dxError in x
yAnother real number
dyError in y
resultThe result as a gsl::sf::result object
Returns
Error code on failure

Definition at line 54 of file sf_elementary.hpp.

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
aA real number
xA real number
Returns
The function value

Definition at line 332 of file sf_gamma.hpp.

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
aA real number
xA real number
resultThe result as a gsl::sf::result object
Returns
GSL_SUCCESS or GSL_EDOM or GSL_EOVRFLW

Definition at line 320 of file sf_gamma.hpp.

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
aA real number
xA real number
Returns
The function value

Definition at line 354 of file sf_gamma.hpp.

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
aA real number
xA real number
resultThe result as a gsl::sf::result object
Returns
GSL_SUCCESS or GSL_EDOM

Definition at line 343 of file sf_gamma.hpp.

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
rA real value (distance)
thetaA real value (angle)
xA real value
yA real value
Returns
GSL_SUCCESS

Definition at line 154 of file sf_trig.hpp.

double gsl::sf::pow_int ( double const  x,
int const  n 
)
inline

C++ version of gsl_sf_pow_int().

Parameters
xA real value
nAn integer
Returns
The nth power of x

Definition at line 43 of file sf_pow_int.hpp.

int gsl::sf::pow_int_e ( double  x,
int  n,
result result 
)
inline

C++ version of gsl_sf_pow_int_e().

Parameters
xA real value
nAn integer
resultThe result as a gsl::sf::result object
Returns
GSL_SUCCESS

Definition at line 36 of file sf_pow_int.hpp.

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
xA real value
Returns
The function value

Definition at line 82 of file sf_psi.hpp.

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
xA real value
Returns
The function value

Definition at line 168 of file sf_psi.hpp.

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
xA real value
resultThe result as a gsl::sf::result object
Returns
GSL_SUCCESS or GSL_EDOM

Definition at line 155 of file sf_psi.hpp.

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
nAn integer
Returns
The function value

Definition at line 141 of file sf_psi.hpp.

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
nAn integer
resultThe result as a gsl::sf::result object
Returns
GSL_SUCCESS or GSL_EDOM

Definition at line 130 of file sf_psi.hpp.

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
yThe imaginary part
Returns
The function value

Definition at line 105 of file sf_psi.hpp.

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
yThe imaginary part
resultThe result as a gsl::sf::result object
Returns
GSL_SUCCESS

Definition at line 94 of file sf_psi.hpp.

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
xA real value
resultThe 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.

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
nAn integer
Returns
The function value

Definition at line 55 of file sf_psi.hpp.

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
nAn integer
resultThe result as a gsl::sf::result object
Returns
GSL_SUCCESS or GSL_EDOM

Definition at line 42 of file sf_psi.hpp.

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
nAn integer
xA real value
Returns
The function value

Definition at line 197 of file sf_psi.hpp.

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
nAn integer
xA real value
resultThe result as a gsl::sf::result object
Returns
GSL_SUCCESS or GSL_EDOM

Definition at line 183 of file sf_psi.hpp.

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
xA real value
yA real value
rThe distance as a gsl::sf::result object
thetaThe angle as a gsl::sf::result object
Returns
GSL_SUCCESS or GSL_ELOSS

Definition at line 164 of file sf_trig.hpp.

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
reObject of type result_e10
rObject of type result
Returns
Error code

Definition at line 41 of file sf_result.hpp.

double gsl::sf::Shi ( double const  x)
inline

C++ version of gsl_sf_Shi().

Shi(x) := Integrate[ Sinh[t]/t, {t,0,x}]

Parameters
xA real number
Returns
The function value

Definition at line 209 of file sf_expint.hpp.

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
xA real number
resultThe 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.

double gsl::sf::Si ( double const  x)
inline

C++ version of gsl_sf_Si().

Si(x) := Integrate[ Sin[t]/t, {t,0,x}]

Parameters
xA real number
Returns
The function value

Definition at line 262 of file sf_expint.hpp.

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
xA real number
resultThe result as a gsl::sf::result object
Returns
GSL_SUCCESS

Definition at line 255 of file sf_expint.hpp.

double gsl::sf::sin ( double const  x)
inline

C++ version of gsl_sf_sin().

Parameters
xA real value
Returns
The function value

Definition at line 41 of file sf_trig.hpp.

int gsl::sf::sin_e ( double  x,
result result 
)
inline

C++ version of gsl_sf_sin_e().

Parameters
xA real value
resultThe result as a gsl::sf::result object
Returns
GSL_SUCCESS

Definition at line 35 of file sf_trig.hpp.

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
xA real value
dxThe error in x
resultThe result as a gsl::sf::result object
Returns
GSL_SUCCESS or GSL_EDOM

Definition at line 174 of file sf_trig.hpp.

double gsl::sf::sinc ( double const  x)
inline

C++ version of gsl_sf_sinc().

Sinc(x) = sin(pi x) / (pi x)

Parameters
xA real value
Returns
The function value

Definition at line 115 of file sf_trig.hpp.

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
xA real value
resultThe result as a gsl::sf::result object
Returns
GSL_SUCCESS

Definition at line 108 of file sf_trig.hpp.

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
xA real value
Returns
The function value

Definition at line 46 of file sf_synchrotron.hpp.

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
xA real value
resultThe 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.

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
xA real value
Returns
The function value

Definition at line 64 of file sf_synchrotron.hpp.

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
xA real value
resultThe 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.

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
nAn integer
xA real number
Returns
The function value

Definition at line 160 of file sf_gamma.hpp.

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
nAn integer
xA real number
resultThe result as a gsl::sf::result object
Returns
GSL_SUCCESS or GSL_EDOM or GSL_EOVRFLW or GSL_EUNDRFLW

Definition at line 149 of file sf_gamma.hpp.

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
xA real value
Returns
The function value

Definition at line 46 of file sf_transport.hpp.

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
xA real value
resultThe result as a gsl::sf::result object
Returns
GSL_SUCCESS or GSL_EDOM

Definition at line 37 of file sf_transport.hpp.

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
xA real value
Returns
The function value

Definition at line 64 of file sf_transport.hpp.

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
xA real value
resultThe 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.

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
xA real value
Returns
The function value

Definition at line 82 of file sf_transport.hpp.

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
xA real value
resultThe 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.

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
xA real value
Returns
The function value

Definition at line 100 of file sf_transport.hpp.

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
xA real value
resultThe 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.

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
sA real value
Returns
The function value

Definition at line 72 of file sf_zeta.hpp.

Referenced by gsl::ran::lognormal().

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
sA real value
resultThe 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.

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
nAn integer
Returns
The function value

Definition at line 50 of file sf_zeta.hpp.

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
nAn integer
resultThe 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.

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
sA real value
Returns
The function value

Definition at line 96 of file sf_zeta.hpp.

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
sA real value
resultThe 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.

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
sA real value
Returns
The function value

Definition at line 120 of file sf_zeta.hpp.

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
sA real value
resultThe 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

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 544 of file sf_gamma.hpp.

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 540 of file sf_gamma.hpp.

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 536 of file sf_gamma.hpp.