# This file was automatically generated by SWIG (https://www.swig.org). # Version 4.2.0 # # Do not make changes to this file unless you know what you are doing - modify # the SWIG interface file instead. package Math::GSL::SF; use base qw(Exporter); use base qw(DynaLoader); package Math::GSL::SFc; bootstrap Math::GSL::SF; package Math::GSL::SF; @EXPORT = qw(); # ---------- BASE METHODS ------------- package Math::GSL::SF; sub TIEHASH { my ($classname,$obj) = @_; return bless $obj, $classname; } sub CLEAR { } sub FIRSTKEY { } sub NEXTKEY { } sub FETCH { my ($self,$field) = @_; my $member_func = "swig_${field}_get"; $self->$member_func(); } sub STORE { my ($self,$field,$newval) = @_; my $member_func = "swig_${field}_set"; $self->$member_func($newval); } sub this { my $ptr = shift; return tied(%$ptr); } # ------- FUNCTION WRAPPERS -------- package Math::GSL::SF; *gsl_error = *Math::GSL::SFc::gsl_error; *gsl_stream_printf = *Math::GSL::SFc::gsl_stream_printf; *gsl_strerror = *Math::GSL::SFc::gsl_strerror; *gsl_set_error_handler = *Math::GSL::SFc::gsl_set_error_handler; *gsl_set_error_handler_off = *Math::GSL::SFc::gsl_set_error_handler_off; *gsl_set_stream_handler = *Math::GSL::SFc::gsl_set_stream_handler; *gsl_set_stream = *Math::GSL::SFc::gsl_set_stream; *gsl_sf_bessel_Jn_array = *Math::GSL::SFc::gsl_sf_bessel_Jn_array; *gsl_sf_bessel_Yn_array = *Math::GSL::SFc::gsl_sf_bessel_Yn_array; *gsl_sf_bessel_In_array = *Math::GSL::SFc::gsl_sf_bessel_In_array; *gsl_sf_bessel_In_scaled_array = *Math::GSL::SFc::gsl_sf_bessel_In_scaled_array; *gsl_sf_bessel_Kn_array = *Math::GSL::SFc::gsl_sf_bessel_Kn_array; *gsl_sf_bessel_Kn_scaled_array = *Math::GSL::SFc::gsl_sf_bessel_Kn_scaled_array; *gsl_sf_bessel_jl_array = *Math::GSL::SFc::gsl_sf_bessel_jl_array; *gsl_sf_bessel_jl_steed_array = *Math::GSL::SFc::gsl_sf_bessel_jl_steed_array; *gsl_sf_bessel_yl_array = *Math::GSL::SFc::gsl_sf_bessel_yl_array; *gsl_sf_bessel_il_scaled_array = *Math::GSL::SFc::gsl_sf_bessel_il_scaled_array; *gsl_sf_airy_Ai_e = *Math::GSL::SFc::gsl_sf_airy_Ai_e; *gsl_sf_airy_Ai = *Math::GSL::SFc::gsl_sf_airy_Ai; *gsl_sf_airy_Bi_e = *Math::GSL::SFc::gsl_sf_airy_Bi_e; *gsl_sf_airy_Bi = *Math::GSL::SFc::gsl_sf_airy_Bi; *gsl_sf_airy_Ai_scaled_e = *Math::GSL::SFc::gsl_sf_airy_Ai_scaled_e; *gsl_sf_airy_Ai_scaled = *Math::GSL::SFc::gsl_sf_airy_Ai_scaled; *gsl_sf_airy_Bi_scaled_e = *Math::GSL::SFc::gsl_sf_airy_Bi_scaled_e; *gsl_sf_airy_Bi_scaled = *Math::GSL::SFc::gsl_sf_airy_Bi_scaled; *gsl_sf_airy_Ai_deriv_e = *Math::GSL::SFc::gsl_sf_airy_Ai_deriv_e; *gsl_sf_airy_Ai_deriv = *Math::GSL::SFc::gsl_sf_airy_Ai_deriv; *gsl_sf_airy_Bi_deriv_e = *Math::GSL::SFc::gsl_sf_airy_Bi_deriv_e; *gsl_sf_airy_Bi_deriv = *Math::GSL::SFc::gsl_sf_airy_Bi_deriv; *gsl_sf_airy_Ai_deriv_scaled_e = *Math::GSL::SFc::gsl_sf_airy_Ai_deriv_scaled_e; *gsl_sf_airy_Ai_deriv_scaled = *Math::GSL::SFc::gsl_sf_airy_Ai_deriv_scaled; *gsl_sf_airy_Bi_deriv_scaled_e = *Math::GSL::SFc::gsl_sf_airy_Bi_deriv_scaled_e; *gsl_sf_airy_Bi_deriv_scaled = *Math::GSL::SFc::gsl_sf_airy_Bi_deriv_scaled; *gsl_sf_airy_zero_Ai_e = *Math::GSL::SFc::gsl_sf_airy_zero_Ai_e; *gsl_sf_airy_zero_Ai = *Math::GSL::SFc::gsl_sf_airy_zero_Ai; *gsl_sf_airy_zero_Bi_e = *Math::GSL::SFc::gsl_sf_airy_zero_Bi_e; *gsl_sf_airy_zero_Bi = *Math::GSL::SFc::gsl_sf_airy_zero_Bi; *gsl_sf_airy_zero_Ai_deriv_e = *Math::GSL::SFc::gsl_sf_airy_zero_Ai_deriv_e; *gsl_sf_airy_zero_Ai_deriv = *Math::GSL::SFc::gsl_sf_airy_zero_Ai_deriv; *gsl_sf_airy_zero_Bi_deriv_e = *Math::GSL::SFc::gsl_sf_airy_zero_Bi_deriv_e; *gsl_sf_airy_zero_Bi_deriv = *Math::GSL::SFc::gsl_sf_airy_zero_Bi_deriv; *gsl_sf_bessel_J0_e = *Math::GSL::SFc::gsl_sf_bessel_J0_e; *gsl_sf_bessel_J0 = *Math::GSL::SFc::gsl_sf_bessel_J0; *gsl_sf_bessel_J1_e = *Math::GSL::SFc::gsl_sf_bessel_J1_e; *gsl_sf_bessel_J1 = *Math::GSL::SFc::gsl_sf_bessel_J1; *gsl_sf_bessel_Jn_e = *Math::GSL::SFc::gsl_sf_bessel_Jn_e; *gsl_sf_bessel_Jn = *Math::GSL::SFc::gsl_sf_bessel_Jn; *gsl_sf_bessel_Y0_e = *Math::GSL::SFc::gsl_sf_bessel_Y0_e; *gsl_sf_bessel_Y0 = *Math::GSL::SFc::gsl_sf_bessel_Y0; *gsl_sf_bessel_Y1_e = *Math::GSL::SFc::gsl_sf_bessel_Y1_e; *gsl_sf_bessel_Y1 = *Math::GSL::SFc::gsl_sf_bessel_Y1; *gsl_sf_bessel_Yn_e = *Math::GSL::SFc::gsl_sf_bessel_Yn_e; *gsl_sf_bessel_Yn = *Math::GSL::SFc::gsl_sf_bessel_Yn; *gsl_sf_bessel_I0_e = *Math::GSL::SFc::gsl_sf_bessel_I0_e; *gsl_sf_bessel_I0 = *Math::GSL::SFc::gsl_sf_bessel_I0; *gsl_sf_bessel_I1_e = *Math::GSL::SFc::gsl_sf_bessel_I1_e; *gsl_sf_bessel_I1 = *Math::GSL::SFc::gsl_sf_bessel_I1; *gsl_sf_bessel_In_e = *Math::GSL::SFc::gsl_sf_bessel_In_e; *gsl_sf_bessel_In = *Math::GSL::SFc::gsl_sf_bessel_In; *gsl_sf_bessel_I0_scaled_e = *Math::GSL::SFc::gsl_sf_bessel_I0_scaled_e; *gsl_sf_bessel_I0_scaled = *Math::GSL::SFc::gsl_sf_bessel_I0_scaled; *gsl_sf_bessel_I1_scaled_e = *Math::GSL::SFc::gsl_sf_bessel_I1_scaled_e; *gsl_sf_bessel_I1_scaled = *Math::GSL::SFc::gsl_sf_bessel_I1_scaled; *gsl_sf_bessel_In_scaled_e = *Math::GSL::SFc::gsl_sf_bessel_In_scaled_e; *gsl_sf_bessel_In_scaled = *Math::GSL::SFc::gsl_sf_bessel_In_scaled; *gsl_sf_bessel_K0_e = *Math::GSL::SFc::gsl_sf_bessel_K0_e; *gsl_sf_bessel_K0 = *Math::GSL::SFc::gsl_sf_bessel_K0; *gsl_sf_bessel_K1_e = *Math::GSL::SFc::gsl_sf_bessel_K1_e; *gsl_sf_bessel_K1 = *Math::GSL::SFc::gsl_sf_bessel_K1; *gsl_sf_bessel_Kn_e = *Math::GSL::SFc::gsl_sf_bessel_Kn_e; *gsl_sf_bessel_Kn = *Math::GSL::SFc::gsl_sf_bessel_Kn; *gsl_sf_bessel_K0_scaled_e = *Math::GSL::SFc::gsl_sf_bessel_K0_scaled_e; *gsl_sf_bessel_K0_scaled = *Math::GSL::SFc::gsl_sf_bessel_K0_scaled; *gsl_sf_bessel_K1_scaled_e = *Math::GSL::SFc::gsl_sf_bessel_K1_scaled_e; *gsl_sf_bessel_K1_scaled = *Math::GSL::SFc::gsl_sf_bessel_K1_scaled; *gsl_sf_bessel_Kn_scaled_e = *Math::GSL::SFc::gsl_sf_bessel_Kn_scaled_e; *gsl_sf_bessel_Kn_scaled = *Math::GSL::SFc::gsl_sf_bessel_Kn_scaled; *gsl_sf_bessel_j0_e = *Math::GSL::SFc::gsl_sf_bessel_j0_e; *gsl_sf_bessel_j0 = *Math::GSL::SFc::gsl_sf_bessel_j0; *gsl_sf_bessel_j1_e = *Math::GSL::SFc::gsl_sf_bessel_j1_e; *gsl_sf_bessel_j1 = *Math::GSL::SFc::gsl_sf_bessel_j1; *gsl_sf_bessel_j2_e = *Math::GSL::SFc::gsl_sf_bessel_j2_e; *gsl_sf_bessel_j2 = *Math::GSL::SFc::gsl_sf_bessel_j2; *gsl_sf_bessel_jl_e = *Math::GSL::SFc::gsl_sf_bessel_jl_e; *gsl_sf_bessel_jl = *Math::GSL::SFc::gsl_sf_bessel_jl; *gsl_sf_bessel_y0_e = *Math::GSL::SFc::gsl_sf_bessel_y0_e; *gsl_sf_bessel_y0 = *Math::GSL::SFc::gsl_sf_bessel_y0; *gsl_sf_bessel_y1_e = *Math::GSL::SFc::gsl_sf_bessel_y1_e; *gsl_sf_bessel_y1 = *Math::GSL::SFc::gsl_sf_bessel_y1; *gsl_sf_bessel_y2_e = *Math::GSL::SFc::gsl_sf_bessel_y2_e; *gsl_sf_bessel_y2 = *Math::GSL::SFc::gsl_sf_bessel_y2; *gsl_sf_bessel_yl_e = *Math::GSL::SFc::gsl_sf_bessel_yl_e; *gsl_sf_bessel_yl = *Math::GSL::SFc::gsl_sf_bessel_yl; *gsl_sf_bessel_i0_scaled_e = *Math::GSL::SFc::gsl_sf_bessel_i0_scaled_e; *gsl_sf_bessel_i0_scaled = *Math::GSL::SFc::gsl_sf_bessel_i0_scaled; *gsl_sf_bessel_i1_scaled_e = *Math::GSL::SFc::gsl_sf_bessel_i1_scaled_e; *gsl_sf_bessel_i1_scaled = *Math::GSL::SFc::gsl_sf_bessel_i1_scaled; *gsl_sf_bessel_i2_scaled_e = *Math::GSL::SFc::gsl_sf_bessel_i2_scaled_e; *gsl_sf_bessel_i2_scaled = *Math::GSL::SFc::gsl_sf_bessel_i2_scaled; *gsl_sf_bessel_il_scaled_e = *Math::GSL::SFc::gsl_sf_bessel_il_scaled_e; *gsl_sf_bessel_il_scaled = *Math::GSL::SFc::gsl_sf_bessel_il_scaled; *gsl_sf_bessel_k0_scaled_e = *Math::GSL::SFc::gsl_sf_bessel_k0_scaled_e; *gsl_sf_bessel_k0_scaled = *Math::GSL::SFc::gsl_sf_bessel_k0_scaled; *gsl_sf_bessel_k1_scaled_e = *Math::GSL::SFc::gsl_sf_bessel_k1_scaled_e; *gsl_sf_bessel_k1_scaled = *Math::GSL::SFc::gsl_sf_bessel_k1_scaled; *gsl_sf_bessel_k2_scaled_e = *Math::GSL::SFc::gsl_sf_bessel_k2_scaled_e; *gsl_sf_bessel_k2_scaled = *Math::GSL::SFc::gsl_sf_bessel_k2_scaled; *gsl_sf_bessel_kl_scaled_e = *Math::GSL::SFc::gsl_sf_bessel_kl_scaled_e; *gsl_sf_bessel_kl_scaled = *Math::GSL::SFc::gsl_sf_bessel_kl_scaled; *gsl_sf_bessel_Jnu_e = *Math::GSL::SFc::gsl_sf_bessel_Jnu_e; *gsl_sf_bessel_Jnu = *Math::GSL::SFc::gsl_sf_bessel_Jnu; *gsl_sf_bessel_Ynu_e = *Math::GSL::SFc::gsl_sf_bessel_Ynu_e; *gsl_sf_bessel_Ynu = *Math::GSL::SFc::gsl_sf_bessel_Ynu; *gsl_sf_bessel_sequence_Jnu_e = *Math::GSL::SFc::gsl_sf_bessel_sequence_Jnu_e; *gsl_sf_bessel_Inu_scaled_e = *Math::GSL::SFc::gsl_sf_bessel_Inu_scaled_e; *gsl_sf_bessel_Inu_scaled = *Math::GSL::SFc::gsl_sf_bessel_Inu_scaled; *gsl_sf_bessel_Inu_e = *Math::GSL::SFc::gsl_sf_bessel_Inu_e; *gsl_sf_bessel_Inu = *Math::GSL::SFc::gsl_sf_bessel_Inu; *gsl_sf_bessel_Knu_scaled_e = *Math::GSL::SFc::gsl_sf_bessel_Knu_scaled_e; *gsl_sf_bessel_Knu_scaled = *Math::GSL::SFc::gsl_sf_bessel_Knu_scaled; *gsl_sf_bessel_Knu_scaled_e10_e = *Math::GSL::SFc::gsl_sf_bessel_Knu_scaled_e10_e; *gsl_sf_bessel_Knu_e = *Math::GSL::SFc::gsl_sf_bessel_Knu_e; *gsl_sf_bessel_Knu = *Math::GSL::SFc::gsl_sf_bessel_Knu; *gsl_sf_bessel_lnKnu_e = *Math::GSL::SFc::gsl_sf_bessel_lnKnu_e; *gsl_sf_bessel_lnKnu = *Math::GSL::SFc::gsl_sf_bessel_lnKnu; *gsl_sf_bessel_zero_J0_e = *Math::GSL::SFc::gsl_sf_bessel_zero_J0_e; *gsl_sf_bessel_zero_J0 = *Math::GSL::SFc::gsl_sf_bessel_zero_J0; *gsl_sf_bessel_zero_J1_e = *Math::GSL::SFc::gsl_sf_bessel_zero_J1_e; *gsl_sf_bessel_zero_J1 = *Math::GSL::SFc::gsl_sf_bessel_zero_J1; *gsl_sf_bessel_zero_Jnu_e = *Math::GSL::SFc::gsl_sf_bessel_zero_Jnu_e; *gsl_sf_bessel_zero_Jnu = *Math::GSL::SFc::gsl_sf_bessel_zero_Jnu; *gsl_sf_clausen_e = *Math::GSL::SFc::gsl_sf_clausen_e; *gsl_sf_clausen = *Math::GSL::SFc::gsl_sf_clausen; *gsl_sf_hydrogenicR_1_e = *Math::GSL::SFc::gsl_sf_hydrogenicR_1_e; *gsl_sf_hydrogenicR_1 = *Math::GSL::SFc::gsl_sf_hydrogenicR_1; *gsl_sf_hydrogenicR_e = *Math::GSL::SFc::gsl_sf_hydrogenicR_e; *gsl_sf_hydrogenicR = *Math::GSL::SFc::gsl_sf_hydrogenicR; *gsl_sf_coulomb_wave_FG_e = *Math::GSL::SFc::gsl_sf_coulomb_wave_FG_e; *gsl_sf_coulomb_wave_F_array = *Math::GSL::SFc::gsl_sf_coulomb_wave_F_array; *gsl_sf_coulomb_wave_FG_array = *Math::GSL::SFc::gsl_sf_coulomb_wave_FG_array; *gsl_sf_coulomb_wave_FGp_array = *Math::GSL::SFc::gsl_sf_coulomb_wave_FGp_array; *gsl_sf_coulomb_wave_sphF_array = *Math::GSL::SFc::gsl_sf_coulomb_wave_sphF_array; *gsl_sf_coulomb_CL_e = *Math::GSL::SFc::gsl_sf_coulomb_CL_e; *gsl_sf_coulomb_CL_array = *Math::GSL::SFc::gsl_sf_coulomb_CL_array; *gsl_sf_coupling_3j_e = *Math::GSL::SFc::gsl_sf_coupling_3j_e; *gsl_sf_coupling_3j = *Math::GSL::SFc::gsl_sf_coupling_3j; *gsl_sf_coupling_6j_e = *Math::GSL::SFc::gsl_sf_coupling_6j_e; *gsl_sf_coupling_6j = *Math::GSL::SFc::gsl_sf_coupling_6j; *gsl_sf_coupling_RacahW_e = *Math::GSL::SFc::gsl_sf_coupling_RacahW_e; *gsl_sf_coupling_RacahW = *Math::GSL::SFc::gsl_sf_coupling_RacahW; *gsl_sf_coupling_9j_e = *Math::GSL::SFc::gsl_sf_coupling_9j_e; *gsl_sf_coupling_9j = *Math::GSL::SFc::gsl_sf_coupling_9j; *gsl_sf_coupling_6j_INCORRECT_e = *Math::GSL::SFc::gsl_sf_coupling_6j_INCORRECT_e; *gsl_sf_coupling_6j_INCORRECT = *Math::GSL::SFc::gsl_sf_coupling_6j_INCORRECT; *gsl_sf_dawson_e = *Math::GSL::SFc::gsl_sf_dawson_e; *gsl_sf_dawson = *Math::GSL::SFc::gsl_sf_dawson; *gsl_sf_debye_1_e = *Math::GSL::SFc::gsl_sf_debye_1_e; *gsl_sf_debye_1 = *Math::GSL::SFc::gsl_sf_debye_1; *gsl_sf_debye_2_e = *Math::GSL::SFc::gsl_sf_debye_2_e; *gsl_sf_debye_2 = *Math::GSL::SFc::gsl_sf_debye_2; *gsl_sf_debye_3_e = *Math::GSL::SFc::gsl_sf_debye_3_e; *gsl_sf_debye_3 = *Math::GSL::SFc::gsl_sf_debye_3; *gsl_sf_debye_4_e = *Math::GSL::SFc::gsl_sf_debye_4_e; *gsl_sf_debye_4 = *Math::GSL::SFc::gsl_sf_debye_4; *gsl_sf_debye_5_e = *Math::GSL::SFc::gsl_sf_debye_5_e; *gsl_sf_debye_5 = *Math::GSL::SFc::gsl_sf_debye_5; *gsl_sf_debye_6_e = *Math::GSL::SFc::gsl_sf_debye_6_e; *gsl_sf_debye_6 = *Math::GSL::SFc::gsl_sf_debye_6; *gsl_sf_dilog_e = *Math::GSL::SFc::gsl_sf_dilog_e; *gsl_sf_dilog = *Math::GSL::SFc::gsl_sf_dilog; *gsl_sf_complex_dilog_xy_e = *Math::GSL::SFc::gsl_sf_complex_dilog_xy_e; *gsl_sf_complex_dilog_e = *Math::GSL::SFc::gsl_sf_complex_dilog_e; *gsl_sf_complex_spence_xy_e = *Math::GSL::SFc::gsl_sf_complex_spence_xy_e; *gsl_sf_multiply_e = *Math::GSL::SFc::gsl_sf_multiply_e; *gsl_sf_multiply = *Math::GSL::SFc::gsl_sf_multiply; *gsl_sf_multiply_err_e = *Math::GSL::SFc::gsl_sf_multiply_err_e; *gsl_sf_ellint_Kcomp_e = *Math::GSL::SFc::gsl_sf_ellint_Kcomp_e; *gsl_sf_ellint_Kcomp = *Math::GSL::SFc::gsl_sf_ellint_Kcomp; *gsl_sf_ellint_Ecomp_e = *Math::GSL::SFc::gsl_sf_ellint_Ecomp_e; *gsl_sf_ellint_Ecomp = *Math::GSL::SFc::gsl_sf_ellint_Ecomp; *gsl_sf_ellint_Pcomp_e = *Math::GSL::SFc::gsl_sf_ellint_Pcomp_e; *gsl_sf_ellint_Pcomp = *Math::GSL::SFc::gsl_sf_ellint_Pcomp; *gsl_sf_ellint_Dcomp_e = *Math::GSL::SFc::gsl_sf_ellint_Dcomp_e; *gsl_sf_ellint_Dcomp = *Math::GSL::SFc::gsl_sf_ellint_Dcomp; *gsl_sf_ellint_F_e = *Math::GSL::SFc::gsl_sf_ellint_F_e; *gsl_sf_ellint_F = *Math::GSL::SFc::gsl_sf_ellint_F; *gsl_sf_ellint_E_e = *Math::GSL::SFc::gsl_sf_ellint_E_e; *gsl_sf_ellint_E = *Math::GSL::SFc::gsl_sf_ellint_E; *gsl_sf_ellint_P_e = *Math::GSL::SFc::gsl_sf_ellint_P_e; *gsl_sf_ellint_P = *Math::GSL::SFc::gsl_sf_ellint_P; *gsl_sf_ellint_RC_e = *Math::GSL::SFc::gsl_sf_ellint_RC_e; *gsl_sf_ellint_RC = *Math::GSL::SFc::gsl_sf_ellint_RC; *gsl_sf_ellint_RD_e = *Math::GSL::SFc::gsl_sf_ellint_RD_e; *gsl_sf_ellint_RD = *Math::GSL::SFc::gsl_sf_ellint_RD; *gsl_sf_ellint_RF_e = *Math::GSL::SFc::gsl_sf_ellint_RF_e; *gsl_sf_ellint_RF = *Math::GSL::SFc::gsl_sf_ellint_RF; *gsl_sf_ellint_RJ_e = *Math::GSL::SFc::gsl_sf_ellint_RJ_e; *gsl_sf_ellint_RJ = *Math::GSL::SFc::gsl_sf_ellint_RJ; *gsl_sf_elljac_e = *Math::GSL::SFc::gsl_sf_elljac_e; *gsl_sf_erfc_e = *Math::GSL::SFc::gsl_sf_erfc_e; *gsl_sf_erfc = *Math::GSL::SFc::gsl_sf_erfc; *gsl_sf_log_erfc_e = *Math::GSL::SFc::gsl_sf_log_erfc_e; *gsl_sf_log_erfc = *Math::GSL::SFc::gsl_sf_log_erfc; *gsl_sf_erf_e = *Math::GSL::SFc::gsl_sf_erf_e; *gsl_sf_erf = *Math::GSL::SFc::gsl_sf_erf; *gsl_sf_erf_Z_e = *Math::GSL::SFc::gsl_sf_erf_Z_e; *gsl_sf_erf_Q_e = *Math::GSL::SFc::gsl_sf_erf_Q_e; *gsl_sf_erf_Z = *Math::GSL::SFc::gsl_sf_erf_Z; *gsl_sf_erf_Q = *Math::GSL::SFc::gsl_sf_erf_Q; *gsl_sf_hazard_e = *Math::GSL::SFc::gsl_sf_hazard_e; *gsl_sf_hazard = *Math::GSL::SFc::gsl_sf_hazard; *gsl_sf_exp_e = *Math::GSL::SFc::gsl_sf_exp_e; *gsl_sf_exp = *Math::GSL::SFc::gsl_sf_exp; *gsl_sf_exp_e10_e = *Math::GSL::SFc::gsl_sf_exp_e10_e; *gsl_sf_exp_mult_e = *Math::GSL::SFc::gsl_sf_exp_mult_e; *gsl_sf_exp_mult = *Math::GSL::SFc::gsl_sf_exp_mult; *gsl_sf_exp_mult_e10_e = *Math::GSL::SFc::gsl_sf_exp_mult_e10_e; *gsl_sf_expm1_e = *Math::GSL::SFc::gsl_sf_expm1_e; *gsl_sf_expm1 = *Math::GSL::SFc::gsl_sf_expm1; *gsl_sf_exprel_e = *Math::GSL::SFc::gsl_sf_exprel_e; *gsl_sf_exprel = *Math::GSL::SFc::gsl_sf_exprel; *gsl_sf_exprel_2_e = *Math::GSL::SFc::gsl_sf_exprel_2_e; *gsl_sf_exprel_2 = *Math::GSL::SFc::gsl_sf_exprel_2; *gsl_sf_exprel_n_e = *Math::GSL::SFc::gsl_sf_exprel_n_e; *gsl_sf_exprel_n = *Math::GSL::SFc::gsl_sf_exprel_n; *gsl_sf_exprel_n_CF_e = *Math::GSL::SFc::gsl_sf_exprel_n_CF_e; *gsl_sf_exp_err_e = *Math::GSL::SFc::gsl_sf_exp_err_e; *gsl_sf_exp_err_e10_e = *Math::GSL::SFc::gsl_sf_exp_err_e10_e; *gsl_sf_exp_mult_err_e = *Math::GSL::SFc::gsl_sf_exp_mult_err_e; *gsl_sf_exp_mult_err_e10_e = *Math::GSL::SFc::gsl_sf_exp_mult_err_e10_e; *gsl_sf_expint_E1_e = *Math::GSL::SFc::gsl_sf_expint_E1_e; *gsl_sf_expint_E1 = *Math::GSL::SFc::gsl_sf_expint_E1; *gsl_sf_expint_E2_e = *Math::GSL::SFc::gsl_sf_expint_E2_e; *gsl_sf_expint_E2 = *Math::GSL::SFc::gsl_sf_expint_E2; *gsl_sf_expint_En_e = *Math::GSL::SFc::gsl_sf_expint_En_e; *gsl_sf_expint_En = *Math::GSL::SFc::gsl_sf_expint_En; *gsl_sf_expint_E1_scaled_e = *Math::GSL::SFc::gsl_sf_expint_E1_scaled_e; *gsl_sf_expint_E1_scaled = *Math::GSL::SFc::gsl_sf_expint_E1_scaled; *gsl_sf_expint_E2_scaled_e = *Math::GSL::SFc::gsl_sf_expint_E2_scaled_e; *gsl_sf_expint_E2_scaled = *Math::GSL::SFc::gsl_sf_expint_E2_scaled; *gsl_sf_expint_En_scaled_e = *Math::GSL::SFc::gsl_sf_expint_En_scaled_e; *gsl_sf_expint_En_scaled = *Math::GSL::SFc::gsl_sf_expint_En_scaled; *gsl_sf_expint_Ei_e = *Math::GSL::SFc::gsl_sf_expint_Ei_e; *gsl_sf_expint_Ei = *Math::GSL::SFc::gsl_sf_expint_Ei; *gsl_sf_expint_Ei_scaled_e = *Math::GSL::SFc::gsl_sf_expint_Ei_scaled_e; *gsl_sf_expint_Ei_scaled = *Math::GSL::SFc::gsl_sf_expint_Ei_scaled; *gsl_sf_Shi_e = *Math::GSL::SFc::gsl_sf_Shi_e; *gsl_sf_Shi = *Math::GSL::SFc::gsl_sf_Shi; *gsl_sf_Chi_e = *Math::GSL::SFc::gsl_sf_Chi_e; *gsl_sf_Chi = *Math::GSL::SFc::gsl_sf_Chi; *gsl_sf_expint_3_e = *Math::GSL::SFc::gsl_sf_expint_3_e; *gsl_sf_expint_3 = *Math::GSL::SFc::gsl_sf_expint_3; *gsl_sf_Si_e = *Math::GSL::SFc::gsl_sf_Si_e; *gsl_sf_Si = *Math::GSL::SFc::gsl_sf_Si; *gsl_sf_Ci_e = *Math::GSL::SFc::gsl_sf_Ci_e; *gsl_sf_Ci = *Math::GSL::SFc::gsl_sf_Ci; *gsl_sf_atanint_e = *Math::GSL::SFc::gsl_sf_atanint_e; *gsl_sf_atanint = *Math::GSL::SFc::gsl_sf_atanint; *gsl_sf_fermi_dirac_m1_e = *Math::GSL::SFc::gsl_sf_fermi_dirac_m1_e; *gsl_sf_fermi_dirac_m1 = *Math::GSL::SFc::gsl_sf_fermi_dirac_m1; *gsl_sf_fermi_dirac_0_e = *Math::GSL::SFc::gsl_sf_fermi_dirac_0_e; *gsl_sf_fermi_dirac_0 = *Math::GSL::SFc::gsl_sf_fermi_dirac_0; *gsl_sf_fermi_dirac_1_e = *Math::GSL::SFc::gsl_sf_fermi_dirac_1_e; *gsl_sf_fermi_dirac_1 = *Math::GSL::SFc::gsl_sf_fermi_dirac_1; *gsl_sf_fermi_dirac_2_e = *Math::GSL::SFc::gsl_sf_fermi_dirac_2_e; *gsl_sf_fermi_dirac_2 = *Math::GSL::SFc::gsl_sf_fermi_dirac_2; *gsl_sf_fermi_dirac_int_e = *Math::GSL::SFc::gsl_sf_fermi_dirac_int_e; *gsl_sf_fermi_dirac_int = *Math::GSL::SFc::gsl_sf_fermi_dirac_int; *gsl_sf_fermi_dirac_mhalf_e = *Math::GSL::SFc::gsl_sf_fermi_dirac_mhalf_e; *gsl_sf_fermi_dirac_mhalf = *Math::GSL::SFc::gsl_sf_fermi_dirac_mhalf; *gsl_sf_fermi_dirac_half_e = *Math::GSL::SFc::gsl_sf_fermi_dirac_half_e; *gsl_sf_fermi_dirac_half = *Math::GSL::SFc::gsl_sf_fermi_dirac_half; *gsl_sf_fermi_dirac_3half_e = *Math::GSL::SFc::gsl_sf_fermi_dirac_3half_e; *gsl_sf_fermi_dirac_3half = *Math::GSL::SFc::gsl_sf_fermi_dirac_3half; *gsl_sf_fermi_dirac_inc_0_e = *Math::GSL::SFc::gsl_sf_fermi_dirac_inc_0_e; *gsl_sf_fermi_dirac_inc_0 = *Math::GSL::SFc::gsl_sf_fermi_dirac_inc_0; *gsl_sf_lngamma_e = *Math::GSL::SFc::gsl_sf_lngamma_e; *gsl_sf_lngamma = *Math::GSL::SFc::gsl_sf_lngamma; *gsl_sf_lngamma_sgn_e = *Math::GSL::SFc::gsl_sf_lngamma_sgn_e; *gsl_sf_gamma_e = *Math::GSL::SFc::gsl_sf_gamma_e; *gsl_sf_gamma = *Math::GSL::SFc::gsl_sf_gamma; *gsl_sf_gammastar_e = *Math::GSL::SFc::gsl_sf_gammastar_e; *gsl_sf_gammastar = *Math::GSL::SFc::gsl_sf_gammastar; *gsl_sf_gammainv_e = *Math::GSL::SFc::gsl_sf_gammainv_e; *gsl_sf_gammainv = *Math::GSL::SFc::gsl_sf_gammainv; *gsl_sf_lngamma_complex_e = *Math::GSL::SFc::gsl_sf_lngamma_complex_e; *gsl_sf_taylorcoeff_e = *Math::GSL::SFc::gsl_sf_taylorcoeff_e; *gsl_sf_taylorcoeff = *Math::GSL::SFc::gsl_sf_taylorcoeff; *gsl_sf_fact_e = *Math::GSL::SFc::gsl_sf_fact_e; *gsl_sf_fact = *Math::GSL::SFc::gsl_sf_fact; *gsl_sf_doublefact_e = *Math::GSL::SFc::gsl_sf_doublefact_e; *gsl_sf_doublefact = *Math::GSL::SFc::gsl_sf_doublefact; *gsl_sf_lnfact_e = *Math::GSL::SFc::gsl_sf_lnfact_e; *gsl_sf_lnfact = *Math::GSL::SFc::gsl_sf_lnfact; *gsl_sf_lndoublefact_e = *Math::GSL::SFc::gsl_sf_lndoublefact_e; *gsl_sf_lndoublefact = *Math::GSL::SFc::gsl_sf_lndoublefact; *gsl_sf_lnchoose_e = *Math::GSL::SFc::gsl_sf_lnchoose_e; *gsl_sf_lnchoose = *Math::GSL::SFc::gsl_sf_lnchoose; *gsl_sf_choose_e = *Math::GSL::SFc::gsl_sf_choose_e; *gsl_sf_choose = *Math::GSL::SFc::gsl_sf_choose; *gsl_sf_lnpoch_e = *Math::GSL::SFc::gsl_sf_lnpoch_e; *gsl_sf_lnpoch = *Math::GSL::SFc::gsl_sf_lnpoch; *gsl_sf_lnpoch_sgn_e = *Math::GSL::SFc::gsl_sf_lnpoch_sgn_e; *gsl_sf_poch_e = *Math::GSL::SFc::gsl_sf_poch_e; *gsl_sf_poch = *Math::GSL::SFc::gsl_sf_poch; *gsl_sf_pochrel_e = *Math::GSL::SFc::gsl_sf_pochrel_e; *gsl_sf_pochrel = *Math::GSL::SFc::gsl_sf_pochrel; *gsl_sf_gamma_inc_Q_e = *Math::GSL::SFc::gsl_sf_gamma_inc_Q_e; *gsl_sf_gamma_inc_Q = *Math::GSL::SFc::gsl_sf_gamma_inc_Q; *gsl_sf_gamma_inc_P_e = *Math::GSL::SFc::gsl_sf_gamma_inc_P_e; *gsl_sf_gamma_inc_P = *Math::GSL::SFc::gsl_sf_gamma_inc_P; *gsl_sf_gamma_inc_e = *Math::GSL::SFc::gsl_sf_gamma_inc_e; *gsl_sf_gamma_inc = *Math::GSL::SFc::gsl_sf_gamma_inc; *gsl_sf_lnbeta_e = *Math::GSL::SFc::gsl_sf_lnbeta_e; *gsl_sf_lnbeta = *Math::GSL::SFc::gsl_sf_lnbeta; *gsl_sf_lnbeta_sgn_e = *Math::GSL::SFc::gsl_sf_lnbeta_sgn_e; *gsl_sf_beta_e = *Math::GSL::SFc::gsl_sf_beta_e; *gsl_sf_beta = *Math::GSL::SFc::gsl_sf_beta; *gsl_sf_beta_inc_e = *Math::GSL::SFc::gsl_sf_beta_inc_e; *gsl_sf_beta_inc = *Math::GSL::SFc::gsl_sf_beta_inc; *gsl_sf_gegenpoly_1_e = *Math::GSL::SFc::gsl_sf_gegenpoly_1_e; *gsl_sf_gegenpoly_2_e = *Math::GSL::SFc::gsl_sf_gegenpoly_2_e; *gsl_sf_gegenpoly_3_e = *Math::GSL::SFc::gsl_sf_gegenpoly_3_e; *gsl_sf_gegenpoly_1 = *Math::GSL::SFc::gsl_sf_gegenpoly_1; *gsl_sf_gegenpoly_2 = *Math::GSL::SFc::gsl_sf_gegenpoly_2; *gsl_sf_gegenpoly_3 = *Math::GSL::SFc::gsl_sf_gegenpoly_3; *gsl_sf_gegenpoly_n_e = *Math::GSL::SFc::gsl_sf_gegenpoly_n_e; *gsl_sf_gegenpoly_n = *Math::GSL::SFc::gsl_sf_gegenpoly_n; *gsl_sf_gegenpoly_array = *Math::GSL::SFc::gsl_sf_gegenpoly_array; *gsl_sf_hyperg_0F1_e = *Math::GSL::SFc::gsl_sf_hyperg_0F1_e; *gsl_sf_hyperg_0F1 = *Math::GSL::SFc::gsl_sf_hyperg_0F1; *gsl_sf_hyperg_1F1_int_e = *Math::GSL::SFc::gsl_sf_hyperg_1F1_int_e; *gsl_sf_hyperg_1F1_int = *Math::GSL::SFc::gsl_sf_hyperg_1F1_int; *gsl_sf_hyperg_1F1_e = *Math::GSL::SFc::gsl_sf_hyperg_1F1_e; *gsl_sf_hyperg_1F1 = *Math::GSL::SFc::gsl_sf_hyperg_1F1; *gsl_sf_hyperg_U_int_e = *Math::GSL::SFc::gsl_sf_hyperg_U_int_e; *gsl_sf_hyperg_U_int = *Math::GSL::SFc::gsl_sf_hyperg_U_int; *gsl_sf_hyperg_U_int_e10_e = *Math::GSL::SFc::gsl_sf_hyperg_U_int_e10_e; *gsl_sf_hyperg_U_e = *Math::GSL::SFc::gsl_sf_hyperg_U_e; *gsl_sf_hyperg_U = *Math::GSL::SFc::gsl_sf_hyperg_U; *gsl_sf_hyperg_U_e10_e = *Math::GSL::SFc::gsl_sf_hyperg_U_e10_e; *gsl_sf_hyperg_2F1_e = *Math::GSL::SFc::gsl_sf_hyperg_2F1_e; *gsl_sf_hyperg_2F1 = *Math::GSL::SFc::gsl_sf_hyperg_2F1; *gsl_sf_hyperg_2F1_conj_e = *Math::GSL::SFc::gsl_sf_hyperg_2F1_conj_e; *gsl_sf_hyperg_2F1_conj = *Math::GSL::SFc::gsl_sf_hyperg_2F1_conj; *gsl_sf_hyperg_2F1_renorm_e = *Math::GSL::SFc::gsl_sf_hyperg_2F1_renorm_e; *gsl_sf_hyperg_2F1_renorm = *Math::GSL::SFc::gsl_sf_hyperg_2F1_renorm; *gsl_sf_hyperg_2F1_conj_renorm_e = *Math::GSL::SFc::gsl_sf_hyperg_2F1_conj_renorm_e; *gsl_sf_hyperg_2F1_conj_renorm = *Math::GSL::SFc::gsl_sf_hyperg_2F1_conj_renorm; *gsl_sf_hyperg_2F0_e = *Math::GSL::SFc::gsl_sf_hyperg_2F0_e; *gsl_sf_hyperg_2F0 = *Math::GSL::SFc::gsl_sf_hyperg_2F0; *gsl_sf_laguerre_1_e = *Math::GSL::SFc::gsl_sf_laguerre_1_e; *gsl_sf_laguerre_2_e = *Math::GSL::SFc::gsl_sf_laguerre_2_e; *gsl_sf_laguerre_3_e = *Math::GSL::SFc::gsl_sf_laguerre_3_e; *gsl_sf_laguerre_1 = *Math::GSL::SFc::gsl_sf_laguerre_1; *gsl_sf_laguerre_2 = *Math::GSL::SFc::gsl_sf_laguerre_2; *gsl_sf_laguerre_3 = *Math::GSL::SFc::gsl_sf_laguerre_3; *gsl_sf_laguerre_n_e = *Math::GSL::SFc::gsl_sf_laguerre_n_e; *gsl_sf_laguerre_n = *Math::GSL::SFc::gsl_sf_laguerre_n; *gsl_sf_lambert_W0_e = *Math::GSL::SFc::gsl_sf_lambert_W0_e; *gsl_sf_lambert_W0 = *Math::GSL::SFc::gsl_sf_lambert_W0; *gsl_sf_lambert_Wm1_e = *Math::GSL::SFc::gsl_sf_lambert_Wm1_e; *gsl_sf_lambert_Wm1 = *Math::GSL::SFc::gsl_sf_lambert_Wm1; *gsl_sf_legendre_Pl_e = *Math::GSL::SFc::gsl_sf_legendre_Pl_e; *gsl_sf_legendre_Pl = *Math::GSL::SFc::gsl_sf_legendre_Pl; *gsl_sf_legendre_Pl_array = *Math::GSL::SFc::gsl_sf_legendre_Pl_array; *gsl_sf_legendre_Pl_deriv_array = *Math::GSL::SFc::gsl_sf_legendre_Pl_deriv_array; *gsl_sf_legendre_P1_e = *Math::GSL::SFc::gsl_sf_legendre_P1_e; *gsl_sf_legendre_P2_e = *Math::GSL::SFc::gsl_sf_legendre_P2_e; *gsl_sf_legendre_P3_e = *Math::GSL::SFc::gsl_sf_legendre_P3_e; *gsl_sf_legendre_P1 = *Math::GSL::SFc::gsl_sf_legendre_P1; *gsl_sf_legendre_P2 = *Math::GSL::SFc::gsl_sf_legendre_P2; *gsl_sf_legendre_P3 = *Math::GSL::SFc::gsl_sf_legendre_P3; *gsl_sf_legendre_Q0_e = *Math::GSL::SFc::gsl_sf_legendre_Q0_e; *gsl_sf_legendre_Q0 = *Math::GSL::SFc::gsl_sf_legendre_Q0; *gsl_sf_legendre_Q1_e = *Math::GSL::SFc::gsl_sf_legendre_Q1_e; *gsl_sf_legendre_Q1 = *Math::GSL::SFc::gsl_sf_legendre_Q1; *gsl_sf_legendre_Ql_e = *Math::GSL::SFc::gsl_sf_legendre_Ql_e; *gsl_sf_legendre_Ql = *Math::GSL::SFc::gsl_sf_legendre_Ql; *gsl_sf_legendre_Plm_e = *Math::GSL::SFc::gsl_sf_legendre_Plm_e; *gsl_sf_legendre_Plm = *Math::GSL::SFc::gsl_sf_legendre_Plm; *gsl_sf_legendre_sphPlm_e = *Math::GSL::SFc::gsl_sf_legendre_sphPlm_e; *gsl_sf_legendre_sphPlm = *Math::GSL::SFc::gsl_sf_legendre_sphPlm; *gsl_sf_conicalP_half_e = *Math::GSL::SFc::gsl_sf_conicalP_half_e; *gsl_sf_conicalP_half = *Math::GSL::SFc::gsl_sf_conicalP_half; *gsl_sf_conicalP_mhalf_e = *Math::GSL::SFc::gsl_sf_conicalP_mhalf_e; *gsl_sf_conicalP_mhalf = *Math::GSL::SFc::gsl_sf_conicalP_mhalf; *gsl_sf_conicalP_0_e = *Math::GSL::SFc::gsl_sf_conicalP_0_e; *gsl_sf_conicalP_0 = *Math::GSL::SFc::gsl_sf_conicalP_0; *gsl_sf_conicalP_1_e = *Math::GSL::SFc::gsl_sf_conicalP_1_e; *gsl_sf_conicalP_1 = *Math::GSL::SFc::gsl_sf_conicalP_1; *gsl_sf_conicalP_sph_reg_e = *Math::GSL::SFc::gsl_sf_conicalP_sph_reg_e; *gsl_sf_conicalP_sph_reg = *Math::GSL::SFc::gsl_sf_conicalP_sph_reg; *gsl_sf_conicalP_cyl_reg_e = *Math::GSL::SFc::gsl_sf_conicalP_cyl_reg_e; *gsl_sf_conicalP_cyl_reg = *Math::GSL::SFc::gsl_sf_conicalP_cyl_reg; *gsl_sf_legendre_H3d_0_e = *Math::GSL::SFc::gsl_sf_legendre_H3d_0_e; *gsl_sf_legendre_H3d_0 = *Math::GSL::SFc::gsl_sf_legendre_H3d_0; *gsl_sf_legendre_H3d_1_e = *Math::GSL::SFc::gsl_sf_legendre_H3d_1_e; *gsl_sf_legendre_H3d_1 = *Math::GSL::SFc::gsl_sf_legendre_H3d_1; *gsl_sf_legendre_H3d_e = *Math::GSL::SFc::gsl_sf_legendre_H3d_e; *gsl_sf_legendre_H3d = *Math::GSL::SFc::gsl_sf_legendre_H3d; *gsl_sf_legendre_H3d_array = *Math::GSL::SFc::gsl_sf_legendre_H3d_array; *gsl_sf_log_e = *Math::GSL::SFc::gsl_sf_log_e; *gsl_sf_log = *Math::GSL::SFc::gsl_sf_log; *gsl_sf_log_abs_e = *Math::GSL::SFc::gsl_sf_log_abs_e; *gsl_sf_log_abs = *Math::GSL::SFc::gsl_sf_log_abs; *gsl_sf_complex_log_e = *Math::GSL::SFc::gsl_sf_complex_log_e; *gsl_sf_log_1plusx_e = *Math::GSL::SFc::gsl_sf_log_1plusx_e; *gsl_sf_log_1plusx = *Math::GSL::SFc::gsl_sf_log_1plusx; *gsl_sf_log_1plusx_mx_e = *Math::GSL::SFc::gsl_sf_log_1plusx_mx_e; *gsl_sf_log_1plusx_mx = *Math::GSL::SFc::gsl_sf_log_1plusx_mx; *gsl_sf_mathieu_a_array = *Math::GSL::SFc::gsl_sf_mathieu_a_array; *gsl_sf_mathieu_b_array = *Math::GSL::SFc::gsl_sf_mathieu_b_array; *gsl_sf_mathieu_a_coeff = *Math::GSL::SFc::gsl_sf_mathieu_a_coeff; *gsl_sf_mathieu_b_coeff = *Math::GSL::SFc::gsl_sf_mathieu_b_coeff; *gsl_sf_mathieu_alloc = *Math::GSL::SFc::gsl_sf_mathieu_alloc; *gsl_sf_mathieu_free = *Math::GSL::SFc::gsl_sf_mathieu_free; *gsl_sf_mathieu_ce_array = *Math::GSL::SFc::gsl_sf_mathieu_ce_array; *gsl_sf_mathieu_se_array = *Math::GSL::SFc::gsl_sf_mathieu_se_array; *gsl_sf_mathieu_Mc_array = *Math::GSL::SFc::gsl_sf_mathieu_Mc_array; *gsl_sf_mathieu_Ms_array = *Math::GSL::SFc::gsl_sf_mathieu_Ms_array; *gsl_sf_pow_int_e = *Math::GSL::SFc::gsl_sf_pow_int_e; *gsl_sf_pow_int = *Math::GSL::SFc::gsl_sf_pow_int; *gsl_sf_psi_int_e = *Math::GSL::SFc::gsl_sf_psi_int_e; *gsl_sf_psi_int = *Math::GSL::SFc::gsl_sf_psi_int; *gsl_sf_psi_e = *Math::GSL::SFc::gsl_sf_psi_e; *gsl_sf_psi = *Math::GSL::SFc::gsl_sf_psi; *gsl_sf_psi_1piy_e = *Math::GSL::SFc::gsl_sf_psi_1piy_e; *gsl_sf_psi_1piy = *Math::GSL::SFc::gsl_sf_psi_1piy; *gsl_sf_complex_psi_e = *Math::GSL::SFc::gsl_sf_complex_psi_e; *gsl_sf_psi_1_int_e = *Math::GSL::SFc::gsl_sf_psi_1_int_e; *gsl_sf_psi_1_int = *Math::GSL::SFc::gsl_sf_psi_1_int; *gsl_sf_psi_1_e = *Math::GSL::SFc::gsl_sf_psi_1_e; *gsl_sf_psi_1 = *Math::GSL::SFc::gsl_sf_psi_1; *gsl_sf_psi_n_e = *Math::GSL::SFc::gsl_sf_psi_n_e; *gsl_sf_psi_n = *Math::GSL::SFc::gsl_sf_psi_n; *gsl_sf_result_smash_e = *Math::GSL::SFc::gsl_sf_result_smash_e; *gsl_sf_synchrotron_1_e = *Math::GSL::SFc::gsl_sf_synchrotron_1_e; *gsl_sf_synchrotron_1 = *Math::GSL::SFc::gsl_sf_synchrotron_1; *gsl_sf_synchrotron_2_e = *Math::GSL::SFc::gsl_sf_synchrotron_2_e; *gsl_sf_synchrotron_2 = *Math::GSL::SFc::gsl_sf_synchrotron_2; *gsl_sf_transport_2_e = *Math::GSL::SFc::gsl_sf_transport_2_e; *gsl_sf_transport_2 = *Math::GSL::SFc::gsl_sf_transport_2; *gsl_sf_transport_3_e = *Math::GSL::SFc::gsl_sf_transport_3_e; *gsl_sf_transport_3 = *Math::GSL::SFc::gsl_sf_transport_3; *gsl_sf_transport_4_e = *Math::GSL::SFc::gsl_sf_transport_4_e; *gsl_sf_transport_4 = *Math::GSL::SFc::gsl_sf_transport_4; *gsl_sf_transport_5_e = *Math::GSL::SFc::gsl_sf_transport_5_e; *gsl_sf_transport_5 = *Math::GSL::SFc::gsl_sf_transport_5; *gsl_sf_sin_e = *Math::GSL::SFc::gsl_sf_sin_e; *gsl_sf_sin = *Math::GSL::SFc::gsl_sf_sin; *gsl_sf_cos_e = *Math::GSL::SFc::gsl_sf_cos_e; *gsl_sf_cos = *Math::GSL::SFc::gsl_sf_cos; *gsl_sf_hypot_e = *Math::GSL::SFc::gsl_sf_hypot_e; *gsl_sf_hypot = *Math::GSL::SFc::gsl_sf_hypot; *gsl_sf_complex_sin_e = *Math::GSL::SFc::gsl_sf_complex_sin_e; *gsl_sf_complex_cos_e = *Math::GSL::SFc::gsl_sf_complex_cos_e; *gsl_sf_complex_logsin_e = *Math::GSL::SFc::gsl_sf_complex_logsin_e; *gsl_sf_sinc_e = *Math::GSL::SFc::gsl_sf_sinc_e; *gsl_sf_sinc = *Math::GSL::SFc::gsl_sf_sinc; *gsl_sf_lnsinh_e = *Math::GSL::SFc::gsl_sf_lnsinh_e; *gsl_sf_lnsinh = *Math::GSL::SFc::gsl_sf_lnsinh; *gsl_sf_lncosh_e = *Math::GSL::SFc::gsl_sf_lncosh_e; *gsl_sf_lncosh = *Math::GSL::SFc::gsl_sf_lncosh; *gsl_sf_polar_to_rect = *Math::GSL::SFc::gsl_sf_polar_to_rect; *gsl_sf_rect_to_polar = *Math::GSL::SFc::gsl_sf_rect_to_polar; *gsl_sf_sin_err_e = *Math::GSL::SFc::gsl_sf_sin_err_e; *gsl_sf_cos_err_e = *Math::GSL::SFc::gsl_sf_cos_err_e; *gsl_sf_angle_restrict_symm_e = *Math::GSL::SFc::gsl_sf_angle_restrict_symm_e; *gsl_sf_angle_restrict_symm = *Math::GSL::SFc::gsl_sf_angle_restrict_symm; *gsl_sf_angle_restrict_pos_e = *Math::GSL::SFc::gsl_sf_angle_restrict_pos_e; *gsl_sf_angle_restrict_pos = *Math::GSL::SFc::gsl_sf_angle_restrict_pos; *gsl_sf_angle_restrict_symm_err_e = *Math::GSL::SFc::gsl_sf_angle_restrict_symm_err_e; *gsl_sf_angle_restrict_pos_err_e = *Math::GSL::SFc::gsl_sf_angle_restrict_pos_err_e; *gsl_sf_zeta_int_e = *Math::GSL::SFc::gsl_sf_zeta_int_e; *gsl_sf_zeta_int = *Math::GSL::SFc::gsl_sf_zeta_int; *gsl_sf_zeta_e = *Math::GSL::SFc::gsl_sf_zeta_e; *gsl_sf_zeta = *Math::GSL::SFc::gsl_sf_zeta; *gsl_sf_zetam1_e = *Math::GSL::SFc::gsl_sf_zetam1_e; *gsl_sf_zetam1 = *Math::GSL::SFc::gsl_sf_zetam1; *gsl_sf_zetam1_int_e = *Math::GSL::SFc::gsl_sf_zetam1_int_e; *gsl_sf_zetam1_int = *Math::GSL::SFc::gsl_sf_zetam1_int; *gsl_sf_hzeta_e = *Math::GSL::SFc::gsl_sf_hzeta_e; *gsl_sf_hzeta = *Math::GSL::SFc::gsl_sf_hzeta; *gsl_sf_eta_int_e = *Math::GSL::SFc::gsl_sf_eta_int_e; *gsl_sf_eta_int = *Math::GSL::SFc::gsl_sf_eta_int; *gsl_sf_eta_e = *Math::GSL::SFc::gsl_sf_eta_e; *gsl_sf_eta = *Math::GSL::SFc::gsl_sf_eta; ############# Class : Math::GSL::SF::gsl_sf_mathieu_workspace ############## package Math::GSL::SF::gsl_sf_mathieu_workspace; use vars qw(@ISA %OWNER %ITERATORS %BLESSEDMEMBERS); @ISA = qw( Math::GSL::SF ); %OWNER = (); %ITERATORS = (); *swig_size_get = *Math::GSL::SFc::gsl_sf_mathieu_workspace_size_get; *swig_size_set = *Math::GSL::SFc::gsl_sf_mathieu_workspace_size_set; *swig_even_order_get = *Math::GSL::SFc::gsl_sf_mathieu_workspace_even_order_get; *swig_even_order_set = *Math::GSL::SFc::gsl_sf_mathieu_workspace_even_order_set; *swig_odd_order_get = *Math::GSL::SFc::gsl_sf_mathieu_workspace_odd_order_get; *swig_odd_order_set = *Math::GSL::SFc::gsl_sf_mathieu_workspace_odd_order_set; *swig_extra_values_get = *Math::GSL::SFc::gsl_sf_mathieu_workspace_extra_values_get; *swig_extra_values_set = *Math::GSL::SFc::gsl_sf_mathieu_workspace_extra_values_set; *swig_qa_get = *Math::GSL::SFc::gsl_sf_mathieu_workspace_qa_get; *swig_qa_set = *Math::GSL::SFc::gsl_sf_mathieu_workspace_qa_set; *swig_qb_get = *Math::GSL::SFc::gsl_sf_mathieu_workspace_qb_get; *swig_qb_set = *Math::GSL::SFc::gsl_sf_mathieu_workspace_qb_set; *swig_aa_get = *Math::GSL::SFc::gsl_sf_mathieu_workspace_aa_get; *swig_aa_set = *Math::GSL::SFc::gsl_sf_mathieu_workspace_aa_set; *swig_bb_get = *Math::GSL::SFc::gsl_sf_mathieu_workspace_bb_get; *swig_bb_set = *Math::GSL::SFc::gsl_sf_mathieu_workspace_bb_set; *swig_dd_get = *Math::GSL::SFc::gsl_sf_mathieu_workspace_dd_get; *swig_dd_set = *Math::GSL::SFc::gsl_sf_mathieu_workspace_dd_set; *swig_ee_get = *Math::GSL::SFc::gsl_sf_mathieu_workspace_ee_get; *swig_ee_set = *Math::GSL::SFc::gsl_sf_mathieu_workspace_ee_set; *swig_tt_get = *Math::GSL::SFc::gsl_sf_mathieu_workspace_tt_get; *swig_tt_set = *Math::GSL::SFc::gsl_sf_mathieu_workspace_tt_set; *swig_e2_get = *Math::GSL::SFc::gsl_sf_mathieu_workspace_e2_get; *swig_e2_set = *Math::GSL::SFc::gsl_sf_mathieu_workspace_e2_set; *swig_zz_get = *Math::GSL::SFc::gsl_sf_mathieu_workspace_zz_get; *swig_zz_set = *Math::GSL::SFc::gsl_sf_mathieu_workspace_zz_set; *swig_eval_get = *Math::GSL::SFc::gsl_sf_mathieu_workspace_eval_get; *swig_eval_set = *Math::GSL::SFc::gsl_sf_mathieu_workspace_eval_set; *swig_evec_get = *Math::GSL::SFc::gsl_sf_mathieu_workspace_evec_get; *swig_evec_set = *Math::GSL::SFc::gsl_sf_mathieu_workspace_evec_set; *swig_wmat_get = *Math::GSL::SFc::gsl_sf_mathieu_workspace_wmat_get; *swig_wmat_set = *Math::GSL::SFc::gsl_sf_mathieu_workspace_wmat_set; sub new { my $pkg = shift; my $self = Math::GSL::SFc::new_gsl_sf_mathieu_workspace(@_); bless $self, $pkg if defined($self); } sub DESTROY { return unless $_[0]->isa('HASH'); my $self = tied(%{$_[0]}); return unless defined $self; delete $ITERATORS{$self}; if (exists $OWNER{$self}) { Math::GSL::SFc::delete_gsl_sf_mathieu_workspace($self); delete $OWNER{$self}; } } sub DISOWN { my $self = shift; my $ptr = tied(%$self); delete $OWNER{$ptr}; } sub ACQUIRE { my $self = shift; my $ptr = tied(%$self); $OWNER{$ptr} = 1; } ############# Class : Math::GSL::SF::gsl_sf_result_struct ############## package Math::GSL::SF::gsl_sf_result_struct; use vars qw(@ISA %OWNER %ITERATORS %BLESSEDMEMBERS); @ISA = qw( Math::GSL::SF ); %OWNER = (); %ITERATORS = (); *swig_val_get = *Math::GSL::SFc::gsl_sf_result_struct_val_get; *swig_val_set = *Math::GSL::SFc::gsl_sf_result_struct_val_set; *swig_err_get = *Math::GSL::SFc::gsl_sf_result_struct_err_get; *swig_err_set = *Math::GSL::SFc::gsl_sf_result_struct_err_set; sub new { my $pkg = shift; my $self = Math::GSL::SFc::new_gsl_sf_result_struct(@_); bless $self, $pkg if defined($self); } sub DESTROY { return unless $_[0]->isa('HASH'); my $self = tied(%{$_[0]}); return unless defined $self; delete $ITERATORS{$self}; if (exists $OWNER{$self}) { Math::GSL::SFc::delete_gsl_sf_result_struct($self); delete $OWNER{$self}; } } sub DISOWN { my $self = shift; my $ptr = tied(%$self); delete $OWNER{$ptr}; } sub ACQUIRE { my $self = shift; my $ptr = tied(%$self); $OWNER{$ptr} = 1; } ############# Class : Math::GSL::SF::gsl_sf_result_e10_struct ############## package Math::GSL::SF::gsl_sf_result_e10_struct; use vars qw(@ISA %OWNER %ITERATORS %BLESSEDMEMBERS); @ISA = qw( Math::GSL::SF ); %OWNER = (); %ITERATORS = (); *swig_val_get = *Math::GSL::SFc::gsl_sf_result_e10_struct_val_get; *swig_val_set = *Math::GSL::SFc::gsl_sf_result_e10_struct_val_set; *swig_err_get = *Math::GSL::SFc::gsl_sf_result_e10_struct_err_get; *swig_err_set = *Math::GSL::SFc::gsl_sf_result_e10_struct_err_set; *swig_e10_get = *Math::GSL::SFc::gsl_sf_result_e10_struct_e10_get; *swig_e10_set = *Math::GSL::SFc::gsl_sf_result_e10_struct_e10_set; sub new { my $pkg = shift; my $self = Math::GSL::SFc::new_gsl_sf_result_e10_struct(@_); bless $self, $pkg if defined($self); } sub DESTROY { return unless $_[0]->isa('HASH'); my $self = tied(%{$_[0]}); return unless defined $self; delete $ITERATORS{$self}; if (exists $OWNER{$self}) { Math::GSL::SFc::delete_gsl_sf_result_e10_struct($self); delete $OWNER{$self}; } } sub DISOWN { my $self = shift; my $ptr = tied(%$self); delete $OWNER{$ptr}; } sub ACQUIRE { my $self = shift; my $ptr = tied(%$self); $OWNER{$ptr} = 1; } # ------- VARIABLE STUBS -------- package Math::GSL::SF; *GSL_VERSION = *Math::GSL::SFc::GSL_VERSION; *GSL_MAJOR_VERSION = *Math::GSL::SFc::GSL_MAJOR_VERSION; *GSL_MINOR_VERSION = *Math::GSL::SFc::GSL_MINOR_VERSION; *GSL_POSZERO = *Math::GSL::SFc::GSL_POSZERO; *GSL_NEGZERO = *Math::GSL::SFc::GSL_NEGZERO; *GSL_SUCCESS = *Math::GSL::SFc::GSL_SUCCESS; *GSL_FAILURE = *Math::GSL::SFc::GSL_FAILURE; *GSL_CONTINUE = *Math::GSL::SFc::GSL_CONTINUE; *GSL_EDOM = *Math::GSL::SFc::GSL_EDOM; *GSL_ERANGE = *Math::GSL::SFc::GSL_ERANGE; *GSL_EFAULT = *Math::GSL::SFc::GSL_EFAULT; *GSL_EINVAL = *Math::GSL::SFc::GSL_EINVAL; *GSL_EFAILED = *Math::GSL::SFc::GSL_EFAILED; *GSL_EFACTOR = *Math::GSL::SFc::GSL_EFACTOR; *GSL_ESANITY = *Math::GSL::SFc::GSL_ESANITY; *GSL_ENOMEM = *Math::GSL::SFc::GSL_ENOMEM; *GSL_EBADFUNC = *Math::GSL::SFc::GSL_EBADFUNC; *GSL_ERUNAWAY = *Math::GSL::SFc::GSL_ERUNAWAY; *GSL_EMAXITER = *Math::GSL::SFc::GSL_EMAXITER; *GSL_EZERODIV = *Math::GSL::SFc::GSL_EZERODIV; *GSL_EBADTOL = *Math::GSL::SFc::GSL_EBADTOL; *GSL_ETOL = *Math::GSL::SFc::GSL_ETOL; *GSL_EUNDRFLW = *Math::GSL::SFc::GSL_EUNDRFLW; *GSL_EOVRFLW = *Math::GSL::SFc::GSL_EOVRFLW; *GSL_ELOSS = *Math::GSL::SFc::GSL_ELOSS; *GSL_EROUND = *Math::GSL::SFc::GSL_EROUND; *GSL_EBADLEN = *Math::GSL::SFc::GSL_EBADLEN; *GSL_ENOTSQR = *Math::GSL::SFc::GSL_ENOTSQR; *GSL_ESING = *Math::GSL::SFc::GSL_ESING; *GSL_EDIVERGE = *Math::GSL::SFc::GSL_EDIVERGE; *GSL_EUNSUP = *Math::GSL::SFc::GSL_EUNSUP; *GSL_EUNIMPL = *Math::GSL::SFc::GSL_EUNIMPL; *GSL_ECACHE = *Math::GSL::SFc::GSL_ECACHE; *GSL_ETABLE = *Math::GSL::SFc::GSL_ETABLE; *GSL_ENOPROG = *Math::GSL::SFc::GSL_ENOPROG; *GSL_ENOPROGJ = *Math::GSL::SFc::GSL_ENOPROGJ; *GSL_ETOLF = *Math::GSL::SFc::GSL_ETOLF; *GSL_ETOLX = *Math::GSL::SFc::GSL_ETOLX; *GSL_ETOLG = *Math::GSL::SFc::GSL_ETOLG; *GSL_EOF = *Math::GSL::SFc::GSL_EOF; *GSL_PREC_DOUBLE = *Math::GSL::SFc::GSL_PREC_DOUBLE; *GSL_PREC_SINGLE = *Math::GSL::SFc::GSL_PREC_SINGLE; *GSL_PREC_APPROX = *Math::GSL::SFc::GSL_PREC_APPROX; *GSL_MODE_DEFAULT = *Math::GSL::SFc::GSL_MODE_DEFAULT; *GSL_SF_GAMMA_XMAX = *Math::GSL::SFc::GSL_SF_GAMMA_XMAX; *GSL_SF_FACT_NMAX = *Math::GSL::SFc::GSL_SF_FACT_NMAX; *GSL_SF_DOUBLEFACT_NMAX = *Math::GSL::SFc::GSL_SF_DOUBLEFACT_NMAX; *GSL_SF_LEGENDRE_SCHMIDT = *Math::GSL::SFc::GSL_SF_LEGENDRE_SCHMIDT; *GSL_SF_LEGENDRE_SPHARM = *Math::GSL::SFc::GSL_SF_LEGENDRE_SPHARM; *GSL_SF_LEGENDRE_FULL = *Math::GSL::SFc::GSL_SF_LEGENDRE_FULL; *GSL_SF_LEGENDRE_NONE = *Math::GSL::SFc::GSL_SF_LEGENDRE_NONE; *GSL_SF_MATHIEU_COEFF = *Math::GSL::SFc::GSL_SF_MATHIEU_COEFF; @EXPORT_airy = qw/ gsl_sf_airy_Ai_e gsl_sf_airy_Ai gsl_sf_airy_Bi_e gsl_sf_airy_Bi gsl_sf_airy_Ai_scaled_e gsl_sf_airy_Ai_scaled gsl_sf_airy_Bi_scaled_e gsl_sf_airy_Bi_scaled gsl_sf_airy_Ai_deriv_e gsl_sf_airy_Ai_deriv gsl_sf_airy_Bi_deriv_e gsl_sf_airy_Bi_deriv gsl_sf_airy_Ai_deriv_scaled_e gsl_sf_airy_Ai_deriv_scaled gsl_sf_airy_Bi_deriv_scaled_e gsl_sf_airy_Bi_deriv_scaled gsl_sf_airy_zero_Ai_e gsl_sf_airy_zero_Ai gsl_sf_airy_zero_Bi_e gsl_sf_airy_zero_Bi gsl_sf_airy_zero_Ai_deriv_e gsl_sf_airy_zero_Ai_deriv gsl_sf_airy_zero_Bi_deriv_e gsl_sf_airy_zero_Bi_deriv /; @EXPORT_bessel =qw/ gsl_sf_bessel_J0_e gsl_sf_bessel_J0 gsl_sf_bessel_J1_e gsl_sf_bessel_J1 gsl_sf_bessel_Jn_e gsl_sf_bessel_Jn gsl_sf_bessel_Jn_array gsl_sf_bessel_Y0_e gsl_sf_bessel_Y0 gsl_sf_bessel_Y1_e gsl_sf_bessel_Y1 gsl_sf_bessel_Yn_e gsl_sf_bessel_Yn gsl_sf_bessel_Yn_array gsl_sf_bessel_I0_e gsl_sf_bessel_I0 gsl_sf_bessel_I1_e gsl_sf_bessel_I1 gsl_sf_bessel_In_e gsl_sf_bessel_In gsl_sf_bessel_In_array gsl_sf_bessel_I0_scaled_e gsl_sf_bessel_I0_scaled gsl_sf_bessel_I1_scaled_e gsl_sf_bessel_I1_scaled gsl_sf_bessel_In_scaled_e gsl_sf_bessel_In_scaled gsl_sf_bessel_In_scaled_array gsl_sf_bessel_K0_e gsl_sf_bessel_K0 gsl_sf_bessel_K1_e gsl_sf_bessel_K1 gsl_sf_bessel_Kn_e gsl_sf_bessel_Kn gsl_sf_bessel_Kn_array gsl_sf_bessel_K0_scaled_e gsl_sf_bessel_K0_scaled gsl_sf_bessel_K1_scaled_e gsl_sf_bessel_K1_scaled gsl_sf_bessel_Kn_scaled_e gsl_sf_bessel_Kn_scaled gsl_sf_bessel_Kn_scaled_array gsl_sf_bessel_j0_e gsl_sf_bessel_j0 gsl_sf_bessel_j1_e gsl_sf_bessel_j1 gsl_sf_bessel_j2_e gsl_sf_bessel_j2 gsl_sf_bessel_jl_e gsl_sf_bessel_jl gsl_sf_bessel_jl_array gsl_sf_bessel_jl_steed_array gsl_sf_bessel_y0_e gsl_sf_bessel_y0 gsl_sf_bessel_y1_e gsl_sf_bessel_y1 gsl_sf_bessel_y2_e gsl_sf_bessel_y2 gsl_sf_bessel_yl_e gsl_sf_bessel_yl gsl_sf_bessel_yl_array gsl_sf_bessel_i0_scaled_e gsl_sf_bessel_i0_scaled gsl_sf_bessel_i1_scaled_e gsl_sf_bessel_i1_scaled gsl_sf_bessel_i2_scaled_e gsl_sf_bessel_i2_scaled gsl_sf_bessel_il_scaled_e gsl_sf_bessel_il_scaled gsl_sf_bessel_il_scaled_array gsl_sf_bessel_k0_scaled_e gsl_sf_bessel_k0_scaled gsl_sf_bessel_k1_scaled_e gsl_sf_bessel_k1_scaled gsl_sf_bessel_k2_scaled_e gsl_sf_bessel_k2_scaled gsl_sf_bessel_kl_scaled_e gsl_sf_bessel_kl_scaled gsl_sf_bessel_kl_scaled_array gsl_sf_bessel_Jnu_e gsl_sf_bessel_Jnu gsl_sf_bessel_Ynu_e gsl_sf_bessel_Ynu gsl_sf_bessel_sequence_Jnu_e gsl_sf_bessel_Inu_scaled_e gsl_sf_bessel_Inu_scaled gsl_sf_bessel_Inu_e gsl_sf_bessel_Inu gsl_sf_bessel_Knu_scaled_e gsl_sf_bessel_Knu_scaled gsl_sf_bessel_Knu_e gsl_sf_bessel_Knu gsl_sf_bessel_lnKnu_e gsl_sf_bessel_lnKnu gsl_sf_bessel_zero_J0_e gsl_sf_bessel_zero_J0 gsl_sf_bessel_zero_J1_e gsl_sf_bessel_zero_J1 gsl_sf_bessel_zero_Jnu_e gsl_sf_bessel_zero_Jnu /; @EXPORT_clausen = qw/ gsl_sf_clausen_e gsl_sf_clausen /; @EXPORT_hydrogenic = qw/ gsl_sf_hydrogenicR_1_e gsl_sf_hydrogenicR_1 gsl_sf_hydrogenicR_e gsl_sf_hydrogenicR /; @EXPORT_coulumb = qw/ gsl_sf_coulomb_wave_FG_e gsl_sf_coulomb_wave_F_array gsl_sf_coulomb_wave_FG_array gsl_sf_coulomb_wave_FGp_array gsl_sf_coulomb_wave_sphF_array gsl_sf_coulomb_CL_e gsl_sf_coulomb_CL_array /; @EXPORT_coupling = qw/ gsl_sf_coupling_3j_e gsl_sf_coupling_3j gsl_sf_coupling_6j_e gsl_sf_coupling_6j gsl_sf_coupling_RacahW_e gsl_sf_coupling_RacahW gsl_sf_coupling_9j_e gsl_sf_coupling_9j gsl_sf_coupling_6j_INCORRECT_e gsl_sf_coupling_6j_INCORRECT /; @EXPORT_dawson = qw/ gsl_sf_dawson_e gsl_sf_dawson /; @EXPORT_debye = qw/ gsl_sf_debye_1_e gsl_sf_debye_1 gsl_sf_debye_2_e gsl_sf_debye_2 gsl_sf_debye_3_e gsl_sf_debye_3 gsl_sf_debye_4_e gsl_sf_debye_4 gsl_sf_debye_5_e gsl_sf_debye_5 gsl_sf_debye_6_e gsl_sf_debye_6 /; @EXPORT_dilog = qw/ gsl_sf_dilog_e gsl_sf_dilog gsl_sf_complex_dilog_xy_e gsl_sf_complex_dilog_e /; @EXPORT_misc = qw/ gsl_sf_complex_spence_xy_e gsl_sf_multiply_e gsl_sf_multiply gsl_sf_multiply_err_e /; @EXPORT_elliptic = qw/ gsl_sf_ellint_Kcomp_e gsl_sf_ellint_Kcomp gsl_sf_ellint_Ecomp_e gsl_sf_ellint_Ecomp gsl_sf_ellint_Pcomp_e gsl_sf_ellint_Pcomp gsl_sf_ellint_Dcomp_e gsl_sf_ellint_Dcomp gsl_sf_ellint_F_e gsl_sf_ellint_F gsl_sf_ellint_E_e gsl_sf_ellint_E gsl_sf_ellint_P_e gsl_sf_ellint_P gsl_sf_ellint_D_e gsl_sf_ellint_D gsl_sf_ellint_RC_e gsl_sf_ellint_RC gsl_sf_ellint_RD_e gsl_sf_ellint_RD gsl_sf_ellint_RF_e gsl_sf_ellint_RF gsl_sf_ellint_RJ_e gsl_sf_ellint_RJ gsl_sf_elljac_e /; @EXPORT_error = qw/ gsl_sf_erfc_e gsl_sf_erfc gsl_sf_log_erfc_e gsl_sf_log_erfc gsl_sf_erf_e gsl_sf_erf gsl_sf_erf_Z_e gsl_sf_erf_Q_e gsl_sf_erf_Z gsl_sf_erf_Q gsl_sf_hazard_e gsl_sf_hazard /; push @EXPORT_misc, qw/ gsl_sf_exp_e gsl_sf_exp gsl_sf_exp_e10_e gsl_sf_exp_mult_e gsl_sf_exp_mult gsl_sf_exp_mult_e10_e gsl_sf_expm1_e gsl_sf_expm1 gsl_sf_exprel_e gsl_sf_exprel gsl_sf_exprel_2_e gsl_sf_exprel_2 gsl_sf_exprel_n_e gsl_sf_exprel_n gsl_sf_exp_err_e gsl_sf_exp_err_e10_e gsl_sf_exp_mult_err_e gsl_sf_exp_mult_err_e10_e gsl_sf_expint_E1_e gsl_sf_expint_E1 gsl_sf_expint_E2_e gsl_sf_expint_E2 gsl_sf_expint_En_e gsl_sf_expint_En gsl_sf_expint_E1_scaled_e gsl_sf_expint_E1_scaled gsl_sf_expint_E2_scaled_e gsl_sf_expint_E2_scaled gsl_sf_expint_En_scaled_e gsl_sf_expint_En_scaled gsl_sf_expint_Ei_e gsl_sf_expint_Ei gsl_sf_expint_Ei_scaled_e gsl_sf_expint_Ei_scaled gsl_sf_Shi_e gsl_sf_Shi gsl_sf_Chi_e gsl_sf_Chi gsl_sf_expint_3_e gsl_sf_expint_3 gsl_sf_Si_e gsl_sf_Si gsl_sf_Ci_e gsl_sf_Ci /; @EXPORT_fermi_dirac = qw/ gsl_sf_fermi_dirac_m1_e gsl_sf_fermi_dirac_m1 gsl_sf_fermi_dirac_0_e gsl_sf_fermi_dirac_0 gsl_sf_fermi_dirac_1_e gsl_sf_fermi_dirac_1 gsl_sf_fermi_dirac_2_e gsl_sf_fermi_dirac_2 gsl_sf_fermi_dirac_int_e gsl_sf_fermi_dirac_int gsl_sf_fermi_dirac_mhalf_e gsl_sf_fermi_dirac_mhalf gsl_sf_fermi_dirac_half_e gsl_sf_fermi_dirac_half gsl_sf_fermi_dirac_3half_e gsl_sf_fermi_dirac_3half gsl_sf_fermi_dirac_inc_0_e gsl_sf_fermi_dirac_inc_0 /; @EXPORT_legendre = qw/ gsl_sf_legendre_Pl_e gsl_sf_legendre_Pl gsl_sf_legendre_Pl_array gsl_sf_legendre_Pl_deriv_array gsl_sf_legendre_P1_e gsl_sf_legendre_P2_e gsl_sf_legendre_P3_e gsl_sf_legendre_P1 gsl_sf_legendre_P2 gsl_sf_legendre_P3 gsl_sf_legendre_Q0_e gsl_sf_legendre_Q0 gsl_sf_legendre_Q1_e gsl_sf_legendre_Q1 gsl_sf_legendre_Ql_e gsl_sf_legendre_Ql gsl_sf_legendre_Plm_e gsl_sf_legendre_Plm gsl_sf_legendre_Plm_array gsl_sf_legendre_Plm_deriv_array gsl_sf_legendre_sphPlm_e gsl_sf_legendre_sphPlm gsl_sf_legendre_sphPlm_array gsl_sf_legendre_sphPlm_deriv_array gsl_sf_legendre_array_size gsl_sf_legendre_H3d_0_e gsl_sf_legendre_H3d_0 gsl_sf_legendre_H3d_1_e gsl_sf_legendre_H3d_1 gsl_sf_legendre_H3d_e gsl_sf_legendre_H3d gsl_sf_legendre_H3d_array /; @EXPORT_gamma = qw/ gsl_sf_lngamma_e gsl_sf_lngamma gsl_sf_lngamma_sgn_e gsl_sf_gamma_e gsl_sf_gamma gsl_sf_gammastar_e gsl_sf_gammastar gsl_sf_gammainv_e gsl_sf_gammainv gsl_sf_lngamma_complex_e gsl_sf_gamma_inc_Q_e gsl_sf_gamma_inc_Q gsl_sf_gamma_inc_P_e gsl_sf_gamma_inc_P gsl_sf_gamma_inc_e gsl_sf_gamma_inc /; @EXPORT_factorial = qw/ gsl_sf_fact_e gsl_sf_fact gsl_sf_doublefact_e gsl_sf_doublefact gsl_sf_lnfact_e gsl_sf_lnfact gsl_sf_lndoublefact_e gsl_sf_lndoublefact /; @EXPORT_hypergeometric = qw/ gsl_sf_hyperg_0F1_e gsl_sf_hyperg_0F1 gsl_sf_hyperg_1F1_int_e gsl_sf_hyperg_1F1_int gsl_sf_hyperg_1F1_e gsl_sf_hyperg_1F1 gsl_sf_hyperg_U_int_e gsl_sf_hyperg_U_int gsl_sf_hyperg_U_int_e10_e gsl_sf_hyperg_U_e gsl_sf_hyperg_U gsl_sf_hyperg_U_e10_e gsl_sf_hyperg_2F1_e gsl_sf_hyperg_2F1 gsl_sf_hyperg_2F1_conj_e gsl_sf_hyperg_2F1_conj gsl_sf_hyperg_2F1_renorm_e gsl_sf_hyperg_2F1_renorm gsl_sf_hyperg_2F1_conj_renorm_e gsl_sf_hyperg_2F1_conj_renorm gsl_sf_hyperg_2F0_e gsl_sf_hyperg_2F0 /; @EXPORT_laguerre = qw/ gsl_sf_laguerre_1_e gsl_sf_laguerre_2_e gsl_sf_laguerre_3_e gsl_sf_laguerre_1 gsl_sf_laguerre_2 gsl_sf_laguerre_3 gsl_sf_laguerre_n_e gsl_sf_laguerre_n /; push @EXPORT_misc, qw/ gsl_sf_taylorcoeff_e gsl_sf_taylorcoeff gsl_sf_lnchoose_e gsl_sf_lnchoose gsl_sf_choose_e gsl_sf_choose gsl_sf_lnpoch_e gsl_sf_lnpoch gsl_sf_lnpoch_sgn_e gsl_sf_poch_e gsl_sf_poch gsl_sf_pochrel_e gsl_sf_pochrel gsl_sf_lnbeta_e gsl_sf_lnbeta gsl_sf_lnbeta_sgn_e gsl_sf_beta_e gsl_sf_beta gsl_sf_beta_inc_e gsl_sf_beta_inc gsl_sf_gegenpoly_1_e gsl_sf_gegenpoly_2_e gsl_sf_gegenpoly_3_e gsl_sf_gegenpoly_1 gsl_sf_gegenpoly_2 gsl_sf_gegenpoly_3 gsl_sf_gegenpoly_n_e gsl_sf_gegenpoly_n gsl_sf_gegenpoly_array gsl_sf_lambert_W0_e gsl_sf_lambert_W0 gsl_sf_lambert_Wm1_e gsl_sf_lambert_Wm1 gsl_sf_conicalP_half_e gsl_sf_conicalP_half gsl_sf_conicalP_mhalf_e gsl_sf_conicalP_mhalf gsl_sf_conicalP_0_e gsl_sf_conicalP_0 gsl_sf_conicalP_1_e gsl_sf_conicalP_1 gsl_sf_conicalP_sph_reg_e gsl_sf_conicalP_sph_reg gsl_sf_conicalP_cyl_reg_e gsl_sf_conicalP_cyl_reg gsl_sf_log_e gsl_sf_log gsl_sf_log_abs_e gsl_sf_log_abs gsl_sf_complex_log_e gsl_sf_log_1plusx_e gsl_sf_log_1plusx gsl_sf_log_1plusx_mx_e gsl_sf_log_1plusx_mx gsl_sf_pow_int_e gsl_sf_pow_int gsl_sf_psi_int_e gsl_sf_psi_int gsl_sf_psi_e gsl_sf_psi gsl_sf_psi_1piy_e gsl_sf_psi_1piy gsl_sf_complex_psi_e gsl_sf_psi_1_int_e gsl_sf_psi_1_int gsl_sf_psi_1_e gsl_sf_psi_1 gsl_sf_psi_n_e gsl_sf_psi_n gsl_sf_result_smash_e gsl_sf_synchrotron_1_e gsl_sf_synchrotron_1 gsl_sf_synchrotron_2_e gsl_sf_synchrotron_2 /; @EXPORT_mathieu = qw/ gsl_sf_mathieu_a_array gsl_sf_mathieu_b_array gsl_sf_mathieu_a gsl_sf_mathieu_a_e gsl_sf_mathieu_b gsl_sf_mathieu_b_e gsl_sf_mathieu_a_coeff gsl_sf_mathieu_b_coeff gsl_sf_mathieu_alloc gsl_sf_mathieu_free gsl_sf_mathieu_ce gsl_sf_mathieu_ce_e gsl_sf_mathieu_se gsl_sf_mathieu_se_e gsl_sf_mathieu_ce_array gsl_sf_mathieu_se_array gsl_sf_mathieu_Mc gsl_sf_mathieu_Ms gsl_sf_mathieu_Mc_array gsl_sf_mathieu_Ms_array /; @EXPORT_transport = qw/ gsl_sf_transport_2_e gsl_sf_transport_2 gsl_sf_transport_3_e gsl_sf_transport_3 gsl_sf_transport_4_e gsl_sf_transport_4 gsl_sf_transport_5_e gsl_sf_transport_5 /; @EXPORT_trig = qw/ gsl_sf_sin_e gsl_sf_sin gsl_sf_sin_pi_x_e gsl_sf_cos_e gsl_sf_cos_pi_x_e gsl_sf_cos gsl_sf_hypot_e gsl_sf_hypot gsl_sf_complex_sin_e gsl_sf_complex_cos_e gsl_sf_complex_logsin_e gsl_sf_sinc_e gsl_sf_sinc gsl_sf_lnsinh_e gsl_sf_lnsinh gsl_sf_lncosh_e gsl_sf_lncosh gsl_sf_polar_to_rect gsl_sf_rect_to_polar gsl_sf_sin_err_e gsl_sf_cos_err_e gsl_sf_angle_restrict_symm_e gsl_sf_angle_restrict_symm gsl_sf_angle_restrict_pos_e gsl_sf_angle_restrict_pos gsl_sf_angle_restrict_symm_err_e gsl_sf_angle_restrict_pos_err_e gsl_sf_atanint_e gsl_sf_atanint /; @EXPORT_zeta = qw/ gsl_sf_zeta_int_e gsl_sf_zeta_int gsl_sf_zeta_e gsl_sf_zeta gsl_sf_zetam1_e gsl_sf_zetam1 gsl_sf_zetam1_int_e gsl_sf_zetam1_int gsl_sf_hzeta_e gsl_sf_hzeta /; @EXPORT_eta = qw/ gsl_sf_eta_int_e gsl_sf_eta_int gsl_sf_eta_e gsl_sf_eta /; @EXPORT_vars = qw/ GSL_SF_GAMMA_XMAX GSL_SF_FACT_NMAX GSL_SF_DOUBLEFACT_NMAX GSL_SF_MATHIEU_COEFF /; @EXPORT_OK = ( @EXPORT_airy, @EXPORT_bessel, @EXPORT_clausen, @EXPORT_hydrogenic, @EXPORT_coulumb, @EXPORT_coupling, @EXPORT_dawson, @EXPORT_debye, @EXPORT_dilog, @EXPORT_misc, @EXPORT_elliptic, @EXPORT_error, @EXPORT_legendre, @EXPORT_gamma, @EXPORT_transport, @EXPORT_trig, @EXPORT_zeta, @EXPORT_eta, @EXPORT_vars, @EXPORT_mathieu, @EXPORT_hypergeometric ); %EXPORT_TAGS = ( all => [ @EXPORT_OK ], airy => [ @EXPORT_airy ], bessel => [ @EXPORT_bessel ], clausen => [ @EXPORT_clausen ], coulumb => [ @EXPORT_coulumb ], coupling => [ @EXPORT_coupling ], dawson => [ @EXPORT_dawson ], debye => [ @EXPORT_debye ], dilog => [ @EXPORT_dilog ], eta => [ @EXPORT_eta ], elliptic => [ @EXPORT_elliptic ], error => [ @EXPORT_error ], factorial => [ @EXPORT_factorial ], gamma => [ @EXPORT_gamma ], hydrogenic => [ @EXPORT_hydrogenic ], hypergeometric => [ @EXPORT_hypergeometric ], laguerre => [ @EXPORT_laguerre ], legendre => [ @EXPORT_legendre ], mathieu => [ @EXPORT_mathieu ], misc => [ @EXPORT_misc ], transport => [ @EXPORT_transport ], trig => [ @EXPORT_trig ], vars => [ @EXPORT_vars ], zeta => [ @EXPORT_zeta ], ); __END__ =encoding utf8 =head1 NAME Math::GSL::SF - Special Functions =head1 SYNOPSIS use Math::GSL::SF qw/:all/; =head1 DESCRIPTION This module contains a data structure named gsl_sf_result. To create a new one use $r = Math::GSL::SF::gsl_sf_result_struct->new; You can then access the elements of the structure in this way : my $val = $r->{val}; my $error = $r->{err}; Here is a list of all included functions: =over =item C =item C These routines compute the Airy function Ai($x) with an accuracy specified by $mode. $mode should be $GSL_PREC_DOUBLE, $GSL_PREC_SINGLE or $GSL_PREC_APPROX. $result is a gsl_sf_result structure. =back =over =item C =item C These routines compute the Airy function Bi($x) with an accuracy specified by $mode. $mode should be $GSL_PREC_DOUBLE, $GSL_PREC_SINGLE or $GSL_PREC_APPROX. $result is a gsl_sf_result structure. =back =over =item C =item C These routines compute a scaled version of the Airy function S_A($x) Ai($x). For $x>0 the scaling factor S_A($x) is \exp(+(2/3) $x**(3/2)), and is 1 for $x<0. $result is a gsl_sf_result structure. =back =over =item C =item C These routines compute a scaled version of the Airy function S_B($x) Bi($x). For $x>0 the scaling factor S_B($x) is exp(-(2/3) $x**(3/2)), and is 1 for $x<0. $result is a gsl_sf_result structure. =back =over =item C =item C These routines compute the Airy function derivative Ai'($x) with an accuracy specified by $mode. $result is a gsl_sf_result structure. =back =over =item C =item C These routines compute the Airy function derivative Bi'($x) with an accuracy specified by $mode. $result is a gsl_sf_result structure. =back =over =item C =item C These routines compute the scaled Airy function derivative S_A(x) Ai'(x). For x>0 the scaling factor S_A(x) is \exp(+(2/3) x^(3/2)), and is 1 for x<0. $result is a gsl_sf_result structure. =back =over =item C =item C These routines compute the scaled Airy function derivative S_B(x) Bi'(x). For x>0 the scaling factor S_B(x) is exp(-(2/3) x^(3/2)), and is 1 for x<0. $result is a gsl_sf_result structure. =back =over =item C =item C These routines compute the location of the s-th zero of the Airy function Ai($x). $result is a gsl_sf_result structure. =back =over =item C =item C These routines compute the location of the s-th zero of the Airy function Bi($x). $result is a gsl_sf_result structure. =back =over =item C =item C These routines compute the location of the s-th zero of the Airy function derivative Ai'(x). $result is a gsl_sf_result structure. =back =over =item C =item C These routines compute the location of the s-th zero of the Airy function derivative Bi'(x). $result is a gsl_sf_result structure. =back =over =item C =item C These routines compute the regular cylindrical Bessel function of zeroth order, J_0($x). $result is a gsl_sf_result structure. =back =over =item C =item C These routines compute the regular cylindrical Bessel function of first order, J_1($x). $result is a gsl_sf_result structure. =back =over =item C =item C These routines compute the regular cylindrical Bessel function of order n, J_n($x). =back =over =item C This routine computes the values of the regular cylindrical Bessel functions J_n($x) for n from $nmin to $nmax inclusive, returning the results in an array reference. The values are computed using recurrence relations for efficiency, and therefore may differ slightly from the exact values. =back =over =item C =item C These routines compute the irregular spherical Bessel function of zeroth order, y_0(x) = -\cos(x)/x. =back =over =item C =item C These routines compute the irregular spherical Bessel function of first order, y_1(x) = -(\cos(x)/x + \sin(x))/x. =back =over =item C($n, $x, $result) =item C These routines compute the irregular cylindrical Bessel function of order $n, Y_n(x), for x>0. =back =over =item C This routine computes the values of the irregular cylindrical Bessel functions Y_n(x) for n from $nmin to $nmax inclusive, returning the results in an array reference. The domain of the function is $x>0. The values are computed using recurrence relations for efficiency, and therefore may differ slightly from the exact values. =back =over =item C =item C These routines compute the regular modified cylindrical Bessel function of zeroth order, I_0(x). =back =over =item C =item C =back =over =item C =item C These routines compute the regular modified cylindrical Bessel function of order $n, I_n(x). =back =over =item C This routine computes the values of the regular modified cylindrical Bessel functions I_n(x) for n from $nmin to $nmax inclusive, returning the results in an array reference. The start of the range nmin must be positive or zero. The values are computed using recurrence relations for efficiency, and therefore may differ slightly from the exact values. =back =over =item C =item C These routines compute the scaled regular modified cylindrical Bessel function of zeroth order \exp(-|x|) I_0(x). =back =over =item C =item C These routines compute the scaled regular modified cylindrical Bessel function of first order \exp(-|x|) I_1(x). =back =over =item C =item C These routines compute the scaled regular modified cylindrical Bessel function of order $n, \exp(-|x|) I_n(x) =back =over =item C This routine computes the values of the scaled regular cylindrical Bessel functions exp(-|$x|) I_n($x) for n from $nmin to $nmax inclusive, returning the results in an array reference. The start of the range nmin must be positive or zero. The values are computed using recurrence relations for efficiency, and therefore may differ slightly from the exact values. =back =over =item C =item C These routines compute the irregular modified cylindrical Bessel function of zeroth order, K_0(x), for x > 0. =back =over =item C =item C These routines compute the irregular modified cylindrical Bessel function of first order, K_1(x), for x > 0. =back =over =item C =item C These routines compute the irregular modified cylindrical Bessel function of order $n, K_n(x), for x > 0. =back =over =item C This routine computes the values of the Irregular Modified Cylindrical Bessel Functions K_n($x) for n from $nmin to $nmax inclusive, returning the results in an array reference. The values are computed using recurrence relations for efficiency, and therefore may differ slightly from the exact values. This function is only defined for positive $x and with throw an exception otherwise. =back =over =item C =item C These routines compute the scaled irregular modified cylindrical Bessel function of zeroth order \exp(x) K_0(x) for x>0. =back =over =item C =item C =back =over =item C =item C =back =over =item C This routine computes the values of the scaled irregular cylindrical Bessel functions exp(x) K_n(x) for n from nmin to nmax inclusive, storing the results in the array result_array. The start of the range nmin must be positive or zero. The domain of the function is x>0. The values are computed using recurrence relations for efficiency, and therefore may differ slightly from the exact values. =back =over =item C =item C =back =over =item C =item C =back =over =item C =item C =back =over =item C =item C =back =over =item C This routine computes the values of the regular spherical Bessel functions j_l(x) for l from 0 to C<$lmax> inclusive for C<$lmax> >= 0 and $x >= 0, returning the results in an array reference. The values are computed using recurrence relations for efficiency, and therefore may differ slightly from the exact values. =back =over =item C This routine uses Steed’s method to compute the values of the regular spherical Bessel functions j_l(x) for l from 0 to $lmax inclusive for $lmax >= 0 and $x >= 0, storing the results in the array result_array. The Steed/Barnett algorithm is described in Comp. Phys. Comm. 21, 297 (1981). Steed’s method is more stable than the recurrence used in the other functions but is also slower. =back =over =item C =item C =back =over =item C =item C =back =over =item C =item C =back =over =item C =item C =back =over =item C This routine computes the values of the irregular spherical Bessel functions y_l(x) for l from 0 to $lmax inclusive for lmax >= 0, returning the results in an array reference. The values are computed using recurrence relations for efficiency, and therefore may differ slightly from the exact values. =back =over =item C =item C =back =over =item C =item C =back =over =item C =item C =back =over =item C =item C =back =over =item C This routine computes the values of the scaled regular modified spherical Bessel functions exp(-|x|) i_l(x) for l from 0 to $lmax inclusive for $lmax >= 0, returning the results in an array reference. The values are computed using recurrence relations for efficiency, and therefore may differ slightly from the exact values. =back =over =item C =item C =back =over =item C =item C =back =over =item C =item C =back =over =item C =item C =back =over =item C This routine computes the values of the scaled irregular modified spherical Bessel functions exp($x) k_l($x) for l from 0 to lmax inclusive for $lmax >= 0 and $x>0, returning the results in an array reference. The values are computed using recurrence relations for efficiency, and therefore may differ slightly from the exact values. =back =over =item C =item C =back =over =item C =back =over =item C =item C =back =over =item C =item C =back =over =item C =item C =back =over =item C =item C =back =over =item C =item C =back =over =item C =item C =back =over =item C =item C =back =over =item C =item C =back =over =item C =item C =back =over =item C =item C =back =over =item C =item C =back =over =item C =item C =back =over =item C - This function computes the Coulomb wave functions F_L(\eta,x), G_{L-k}(\eta,x) and their derivatives F'_L(\eta,x), G'_{L-k}(\eta,x) with respect to $x. The parameters are restricted to L, L-k > -1/2, x > 0 and integer $k. Note that L itself is not restricted to being an integer. The results are stored in the parameters $F, $G for the function values and $Fp, $Gp for the derivative values. $F, $G, $Fp, $Gp are all gsl_result structs. If an overflow occurs, $GSL_EOVRFLW is returned and scaling exponents are returned as second and third values. =item C - =item C - =item C - =item C - =item C - This function computes the Coulomb wave function normalization constant C_L($eta) for $L > -1. =item C - =back =over =item C =item C These routines compute the Wigner 3-j coefficient, (ja jb jc ma mb mc) where the arguments are given in half-integer units, ja = $two_ja/2, ma = $two_ma/2, etc. =back =over =item C =item C These routines compute the Wigner 6-j coefficient, {ja jb jc jd je jf} where the arguments are given in half-integer units, ja = $two_ja/2, ma = $two_ma/2, etc. =back =over =item C =item C =back =over =item C =item C These routines compute the Wigner 9-j coefficient, {ja jb jc jd je jf jg jh ji} where the arguments are given in half-integer units, ja = two_ja/2, ma = two_ma/2, etc. =back =over =item C =item C These routines compute the value of Dawson's integral for $x. =back =over =item C =item C These routines compute the first-order Debye function D_1(x) = (1/x) \int_0^x dt (t/(e^t - 1)). =back =over =item C =item C These routines compute the second-order Debye function D_2(x) = (2/x^2) \int_0^x dt (t^2/(e^t - 1)). =back =over =item C =item C These routines compute the third-order Debye function D_3(x) = (3/x^3) \int_0^x dt (t^3/(e^t - 1)). =back =over =item C =item C These routines compute the fourth-order Debye function D_4(x) = (4/x^4) \int_0^x dt (t^4/(e^t - 1)). =back =over =item C =item C These routines compute the fifth-order Debye function D_5(x) = (5/x^5) \int_0^x dt (t^5/(e^t - 1)). =back =over =item C =item C These routines compute the sixth-order Debye function D_6(x) = (6/x^6) \int_0^x dt (t^6/(e^t - 1)). =back =over =item C =item C These routines compute the dilogarithm for a real argument. In Lewin's notation this is Li_2(x), the real part of the dilogarithm of a real x. It is defined by the integral representation Li_2(x) = - \Re \int_0^x ds \log(1-s) / s. Note that \Im(Li_2(x)) = 0 for x <= 1, and -\pi\log(x) for x > 1. Note that Abramowitz & Stegun refer to the Spence integral S(x)=Li_2(1-x) as the dilogarithm rather than Li_2(x). =back =over =item C - =item C - This function computes the full complex-valued dilogarithm for the complex argument z = r \exp(i \theta). The real and imaginary parts of the result are returned in the $result_re and $result_im gsl_result structs. =item C - =back =over =item C =item C - This function multiplies $x and $y storing the product and its associated error in $result. =item C - This function multiplies $x and $y with associated absolute errors $dx and $dy. The product xy +/- xy \sqrt((dx/x)^2 +(dy/y)^2) is stored in $result. =back =over =item C =item C These routines compute the complete elliptic integral K($k) to the accuracy specified by the mode variable mode. Note that Abramowitz & Stegun define this function in terms of the parameter m = k^2. =back =over =item C =item C =back =over =item C =item C =back =over =item C =item C =back =over =item C =item C These routines compute the incomplete elliptic integral F($phi,$k) to the accuracy specified by the mode variable mode. Note that Abramowitz & Stegun define this function in terms of the parameter m = k^2. =back =over =item C =item C These routines compute the incomplete elliptic integral E($phi,$k) to the accuracy specified by the mode variable mode. Note that Abramowitz & Stegun define this function in terms of the parameter m = k^2. =back =over =item C =item C These routines compute the incomplete elliptic integral \Pi(\phi,k,n) to the accuracy specified by the mode variable mode. Note that Abramowitz & Stegun define this function in terms of the parameters m = k^2 and \sin^2(\alpha) = k^2, with the change of sign n \to -n. =back =over =item C =item C These functions compute the incomplete elliptic integral D(\phi,k) which is defined through the Carlson form RD(x,y,z) by the following relation, D(\phi,k,n) = (1/3)(\sin(\phi))^3 RD (1-\sin^2(\phi), 1-k^2 \sin^2(\phi), 1). The argument $n is not used and will be removed in a future release. =back =over =item C =item C These routines compute the incomplete elliptic integral RC($x,$y) to the accuracy specified by the mode variable $mode. =back =over =item C =item C These routines compute the incomplete elliptic integral RD($x,$y,$z) to the accuracy specified by the mode variable $mode. =back =over =item C =item C These routines compute the incomplete elliptic integral RF($x,$y,$z) to the accuracy specified by the mode variable $mode. =back =over =item C =item C These routines compute the incomplete elliptic integral RJ($x,$y,$z,$p) to the accuracy specified by the mode variable $mode. =back =over =item C - This function computes the Jacobian elliptic functions sn(u|m), cn(u|m), dn(u|m) by descending Landen transformations. The function returns 0 if the operation succeded, 1 otherwise and then returns the result of sn, cn and dn in this order. =item C =item C These routines compute the complementary error function erfc(x) = 1 - erf(x) = (2/\sqrt(\pi)) \int_x^\infty \exp(-t^2). =back =over =item C =item C These routines compute the logarithm of the complementary error function \log(\erfc(x)). =back =over =item C =item C These routines compute the error function erf(x), where erf(x) = (2/\sqrt(\pi)) \int_0^x dt \exp(-t^2). =back =over =item C =item C These routines compute the Gaussian probability density function Z(x) = (1/\sqrt{2\pi}) \exp(-x^2/2). =back =over =item C =item C These routines compute the upper tail of the Gaussian probability function Q(x) = (1/\sqrt{2\pi}) \int_x^\infty dt \exp(-t^2/2). The hazard function for the normal distribution, also known as the inverse Mill's ratio, is defined as, h(x) = Z(x)/Q(x) = \sqrt{2/\pi} \exp(-x^2 / 2) / \erfc(x/\sqrt 2) It decreases rapidly as x approaches -\infty and asymptotes to h(x) \sim x as x approaches +\infty. =back =over =item C =item C These routines compute the hazard function for the normal distribution. =back =over =item C =item C These routines provide an exponential function \exp(x) using GSL semantics and error checking. =back =over =item C - =back =over =item C =item C =back =over =item C - =back =over =item C =item C These routines compute the quantity \exp(x)-1 using an algorithm that is accurate for small x. =back =over =item C =item C These routines compute the quantity (\exp(x)-1)/x using an algorithm that is accurate for small x. For small x the algorithm is based on the expansion (\exp(x)-1)/x = 1 + x/2 + x^2/(2*3) + x^3/(2*3*4) + \dots. =back =over =item C =item C These routines compute the quantity 2(\exp(x)-1-x)/x^2 using an algorithm that is accurate for small x. For small x the algorithm is based on the expansion 2(\exp(x)-1-x)/x^2 = 1 + x/3 + x^2/(3*4) + x^3/(3*4*5) + \dots. =back =over =item C =item C These routines compute the N-relative exponential, which is the n-th generalization of the functions gsl_sf_exprel and gsl_sf_exprel2. The N-relative exponential is given by, exprel_N(x) = N!/x^N (\exp(x) - \sum_{k=0}^{N-1} x^k/k!) = 1 + x/(N+1) + x^2/((N+1)(N+2)) + ... = 1F1 (1,1+N,x) =back =over =item C - This function exponentiates $x with an associated absolute error $dx. =item C - =item C - =item C - =back =over =item C =item C These routines compute the exponential integral E_1(x), E_1(x) := \Re \int_1^\infty dt \exp(-xt)/t. =back =over =item C =item C These routines compute the second-order exponential integral E_2(x), E_2(x) := \Re \int_1^\infty dt \exp(-xt)/t^2. =back =over =item C =item C These routines compute the exponential integral E_n(x) of order n, E_n(x) := \Re \int_1^\infty dt \exp(-xt)/t^n. =back =over =item C =item C =back =over =item C =item C =back =over =item C =item C =back =over =item C =item C These routines compute the exponential integral Ei(x), Ei(x) := - PV(\int_{-x}^\infty dt \exp(-t)/t) where PV denotes the principal value of the integral. =back =over =item C =item C =back =over =item C =item C These routines compute the integral Shi(x) = \int_0^x dt \sinh(t)/t. =back =over =item C =item C These routines compute the integral Chi(x) := \Re[ \gamma_E + \log(x) + \int_0^x dt (\cosh[t]-1)/t] , where \gamma_E is the Euler constant (available as $M_EULER from the Math::GSL::Const module). =back =over =item C =item C These routines compute the third-order exponential integral Ei_3(x) = \int_0^xdt \exp(-t^3) for x >= 0. =back =over =item C =item C These routines compute the Sine integral Si(x) = \int_0^x dt \sin(t)/t. =back =over =item C =item C These routines compute the Cosine integral Ci(x) = -\int_x^\infty dt \cos(t)/t for x > 0. =back =over =item C =item C These routines compute the complete Fermi-Dirac integral with an index of -1. This integral is given by F_{-1}(x) = e^x / (1 + e^x). =back =over =item C =item C These routines compute the complete Fermi-Dirac integral with an index of 0. This integral is given by F_0(x) = \ln(1 + e^x). =back =over =item C =item C These routines compute the complete Fermi-Dirac integral with an index of 1, F_1(x) = \int_0^\infty dt (t /(\exp(t-x)+1)). =back =over =item C =item C These routines compute the complete Fermi-Dirac integral with an index of 2, F_2(x) = (1/2) \int_0^\infty dt (t^2 /(\exp(t-x)+1)). =back =over =item C =item C These routines compute the complete Fermi-Dirac integral with an integer index of j, F_j(x) = (1/\Gamma(j+1)) \int_0^\infty dt (t^j /(\exp(t-x)+1)). =back =over =item C =item C These routines compute the complete Fermi-Dirac integral F_{-1/2}(x). =back =over =item C =item C These routines compute the complete Fermi-Dirac integral F_{1/2}(x). =back =over =item C =item C These routines compute the complete Fermi-Dirac integral F_{3/2}(x). =back =over =item C =item C These routines compute the incomplete Fermi-Dirac integral with an index of zero, F_0(x,b) = \ln(1 + e^{b-x}) - (b-x). =back =over =item C =item C These functions evaluate the Legendre polynomial P_l(x) for a specific value of l, x subject to l >= 0, |x| <= 1 =back =over =item C =item C =back =over =item C =item C =item C =item C =item C =item C These functions evaluate the Legendre polynomials P_l(x) using explicit representations for l=1, 2, 3. =back =over =item C =item C These routines compute the Legendre function Q_0(x) for x > -1, x != 1. =back =over =item C =item C These routines compute the Legendre function Q_1(x) for x > -1, x != 1. =back =over =item C =item C These routines compute the Legendre function Q_l(x) for x > -1, x != 1 and l >= 0. =back =over =item C =item C These routines compute the associated Legendre polynomial P_l^m(x) for m >= 0, l >= m, |x| <= 1. =back =over =item C =item C =back =over =item C =item C These routines compute the normalized associated Legendre polynomial $\sqrt{(2l+1)/(4\pi)} \sqrt{(l-m)!/(l+m)!} P_l^m(x)$ suitable for use in spherical harmonics. The parameters must satisfy m >= 0, l >= m, |x| <= 1. Theses routines avoid the overflows that occur for the standard normalization of P_l^m(x). =back =over =item C =item C =back =over =item C - =back =over =item C =item C These routines compute the logarithm of the Gamma function, \log(\Gamma(x)), subject to x not being a negative integer or zero. For x<0 the real part of \log(\Gamma(x)) is returned, which is equivalent to \log(|\Gamma(x)|). The function is computed using the real Lanczos method. =back =over =item C - This routine returns the sign of the gamma function and the logarithm of its magnitude into this order, subject to $x not being a negative integer or zero. The function is computed using the real Lanczos method. The value of the gamma function can be reconstructed using the relation \Gamma(x) = sgn * \exp(resultlg). =back =over =item C =item C =back =over =item C =item C =back =over =item C =item C =back =over =item C =back =over =item C =item C =back =over =item C =item C =back =over =item C =item C =back =over =item C =item C =back =over =item C =item C =back =over =item C =item C =back =over =item C =item C =back =over =item C =item C =back =over =item C =item C =back =over =item C =item C =back =over =item C =item C =back =over =item C =back =over =item C =item C =back =over =item C =item C =back =over =item C =item C =back =over =item C =back =over =item C =item C =back =over =item C =item C =back =over =item C =item C =item C =item C =item C =item C =back =over =item C =item C =back =over =item C =item C =item C =back =over =item C =item C =back =over =item C =item C =back =over =item C =item C =back =over =item C =back =over =item C =item C =back =over =item C =back =over =item C =item C =back =over =item C =item C =back =over =item C =item C =back =over =item C =item C =back =over =item C =item C =back =over =item C =item C =item C =item C =item C =item C =back =over =item C =item C =back =over =item C =item C =back =over =item C =item C =back =over =item C =item C =back =over =item C =item C =back =over =item C =item C =back =over =item C =item C =back =over =item C =item C =back =over =item C =item C =back =over =item C =item C =back =over =item C =item C =back =over =item C =item C =back =over =item C =back =over =item C =item C =back =over =item C =item C =back =over =item C =back =over =item C =item C =back =over =item C =item C =back =over =item C =item C =back =over =item C =item C =back =over =item C =item C =back =over =item C =back =over =item C =back =over =item C =item C =back =over =item C =item C =back =over =item C =item C =back =over =item C =item C =back =over =item C =item C =back =over =item C =item C =back =over =item C =item C =back =over =item C =item C =back =over =item C =back =over =item C =item C =back =over =item C =item C =back =over =item C =item C =back =over =item C =back =over =item C =item C =back =over =item C =item C =back =over =item C =item C =back =over =item C =item C =back =over =item C =item C =back =over =item C =item C =back =over =item C =item C =back =over =item C =item C =back =over =item C =item C =back =over =item C =back =over =item C =back =over =item C =back =over =item C =item C =back =over =item C =item C =back =over =item C =item C =back =over =item C =back =over =item C =back =over =item C =item C =back =over =item C =item C =back =over =item C =item C =back =over =item C =item C =over =item C =item C These routines compute the Arctangent integral, which is defined as AtanInt(x) = \int_0^x dt \arctan(t)/t. =back =item C =item C =item C =item C =item C =item C =item C =item C =item C =item C =item C =item C =item C =back This module also contains the following constants used as mode in various of those functions : =over =item * GSL_PREC_DOUBLE - Double-precision, a relative accuracy of approximately 2 * 10^-16. =item * GSL_PREC_SINGLE - Single-precision, a relative accuracy of approximately 10^-7. =item * GSL_PREC_APPROX - Approximate values, a relative accuracy of approximately 5 * 10^-4. =back You can import the functions that you want to use by giving a space separated list to Math::GSL::SF when you use the package. You can also write use Math::GSL::SF qw/:all/ to use all available functions of the module. Note that the tag names begin with a colon. Other tags are also available, here is a complete list of all tags for this module : =over =item C =item C =item C =item C =item C =item C =item C =item C =item C =item C =item C =item C =item C =item C =item C =item C =item C =item C =item C =item C =item C =item C =back For more informations on the functions, we refer you to the GSL official documentation: L =head1 EXAMPLES This example computes the dilogarithm of 1/10 : use Math::GSL::SF qw/dilog/; my $x = gsl_sf_dilog(0.1); print "gsl_sf_dilog(0.1) = $x\n"; An example using Math::GSL::SF and gnuplot is in the B folder of the source code. =head1 AUTHORS Jonathan "Duke" Leto and Thierry Moisan =head1 COPYRIGHT AND LICENSE Copyright (C) 2008-2024 Jonathan "Duke" Leto and Thierry Moisan This program is free software; you can redistribute it and/or modify it under the same terms as Perl itself. =cut 1;