%perlcode %{
@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_b
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_se
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__
=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 = $r->{err};
Here is a list of all included functions:
=over
=item C<gsl_sf_airy_Ai_e($x, $mode)>
=item C<gsl_sf_airy_Ai($x, $mode, $result)>
- These routines compute the Airy function Ai($x) with an accuracy specified by $mode. $mode should be $GSL_PREC_DOUBLE, $GSL_PREC_SINGLE or $GSL_PREC_APPROX. $result is a gsl_sf_result structure.
=back
=over
=item C<gsl_sf_airy_Bi_e($x, $mode, $result)>
=item C<gsl_sf_airy_Bi($x, $mode)>
- These routines compute the Airy function Bi($x) with an accuracy specified by $mode. $mode should be $GSL_PREC_DOUBLE, $GSL_PREC_SINGLE or $GSL_PREC_APPROX. $result is a gsl_sf_result structure.
=back
=over
=item C<gsl_sf_airy_Ai_scaled_e($x, $mode, $result)>
=item C<gsl_sf_airy_Ai_scaled($x, $mode)>
- These routines compute a scaled version of the Airy function S_A($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. $result is a gsl_sf_result structure.
=back
=over
=item C<gsl_sf_airy_Bi_scaled_e($x, $mode, $result)>
=item C<gsl_sf_airy_Bi_scaled($x, $mode)>
- These routines compute a scaled version of the Airy function S_B($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. $result is a gsl_sf_result structure.
=back
=over
=item C<gsl_sf_airy_Ai_deriv_e($x, $mode, $result)>
=item C<gsl_sf_airy_Ai_deriv($x, $mode)>
- These routines compute the Airy function derivative Ai'($x) with an accuracy specified by $mode. $result is a gsl_sf_result structure.
=back
=over
=item C<gsl_sf_airy_Bi_deriv_e($x, $mode, $result)>
=item C<gsl_sf_airy_Bi_deriv($x, $mode)>
-These routines compute the Airy function derivative Bi'($x) with an accuracy specified by $mode. $result is a gsl_sf_result structure.
=back
=over
=item C<gsl_sf_airy_Ai_deriv_scaled_e($x, $mode, $result)>
=item C<gsl_sf_airy_Ai_deriv_scaled($x, $mode)>
-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. $result is a gsl_sf_result structure.
=back
=over
=item C<gsl_sf_airy_Bi_deriv_scaled_e($x, $mode, $result)>
=item C<gsl_sf_airy_Bi_deriv_scaled($x, $mode)>
-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. $result is a gsl_sf_result structure.
=back
=over
=item C<gsl_sf_airy_zero_Ai_e($s, $result)>
=item C<gsl_sf_airy_zero_Ai($s)>
-These routines compute the location of the s-th zero of the Airy function Ai($x). $result is a gsl_sf_result structure.
=back
=over
=item C<gsl_sf_airy_zero_Bi_e($s, $result)>
=item C<gsl_sf_airy_zero_Bi($s)>
-These routines compute the location of the s-th zero of the Airy function Bi($x). $result is a gsl_sf_result structure.
=back
=over
=item C<gsl_sf_airy_zero_Ai_deriv_e($s, $result)>
=item C<gsl_sf_airy_zero_Ai_deriv($s)>
-These routines compute the location of the s-th zero of the Airy function derivative Ai'(x). $result is a gsl_sf_result structure.
=back
=over
=item C<gsl_sf_airy_zero_Bi_deriv_e($s, $result)>
=item C<gsl_sf_airy_zero_Bi_deriv($s)>
- These routines compute the location of the s-th zero of the Airy function derivative Bi'(x). $result is a gsl_sf_result structure.
=back
=over
=item C<gsl_sf_bessel_J0_e($x, $result)>
=item C<gsl_sf_bessel_J0($x)>
-These routines compute the regular cylindrical Bessel function of zeroth order, J_0($x). $result is a gsl_sf_result structure.
=back
=over
=item C<gsl_sf_bessel_J1_e($x, $result)>
=item C<gsl_sf_bessel_J1($x)>
- These routines compute the regular cylindrical Bessel function of first order, J_1($x). $result is a gsl_sf_result structure.
=back
=over
=item C<gsl_sf_bessel_Jn_e($n, $x, $result)>
=item C<gsl_sf_bessel_Jn($n, $x)>
-These routines compute the regular cylindrical Bessel function of order n, J_n($x).
=back
=over
=item C<gsl_sf_bessel_Jn_array($nmin, $nmax, $x, $result_array)> - This routine computes the values of the regular cylindrical Bessel functions J_n($x) for n from $nmin to $nmax inclusive, storing the results in the array $result_array. The values are computed using recurrence relations for efficiency, and therefore may differ slightly from the exact values.
=back
=over
=item C<gsl_sf_bessel_Y0_e($x, $result)>
=item C<gsl_sf_bessel_Y0($x)>
- These routines compute the irregular spherical Bessel function of zeroth order, y_0(x) = -\cos(x)/x.
=back
=over
=item C<gsl_sf_bessel_Y1_e($x, $result)>
=item C<gsl_sf_bessel_Y1($x)>
-These routines compute the irregular spherical Bessel function of first order, y_1(x) = -(\cos(x)/x + \sin(x))/x.
=back
=over
=item C<gsl_sf_bessel_Yn_e>($n, $x, $result)
=item C<gsl_sf_bessel_Yn($n, $x)>
-These routines compute the irregular cylindrical Bessel function of order $n, Y_n(x), for x>0.
=back
=over
=item C<gsl_sf_bessel_Yn_array>
-
=back
=over
=item C<gsl_sf_bessel_I0_e($x, $result)>
=item C<gsl_sf_bessel_I0($x)>
-These routines compute the regular modified cylindrical Bessel function of zeroth order, I_0(x).
=back
=over
=item C<gsl_sf_bessel_I1_e($x, $result)>
=item C<gsl_sf_bessel_I1($x)>
-These routines compute the regular modified cylindrical Bessel function of first order, I_1(x).
=back
=over
=item C<gsl_sf_bessel_In_e($n, $x, $result)>
=item C<gsl_sf_bessel_In($n, $x)>
-These routines compute the regular modified cylindrical Bessel function of order $n, I_n(x).
=back
=over
=item C<gsl_sf_bessel_In_array>
-
=back
=over
=item C<gsl_sf_bessel_I0_scaled_e($x, $result)>
=item C<gsl_sf_bessel_I0_scaled($x)>
-These routines compute the scaled regular modified cylindrical Bessel function of zeroth order \exp(-|x|) I_0(x).
=back
=over
=item C<gsl_sf_bessel_I1_scaled_e($x, $result)>
=item C<gsl_sf_bessel_I1_scaled($x)>
-These routines compute the scaled regular modified cylindrical Bessel function of first order \exp(-|x|) I_1(x).
=back
=over
=item C<gsl_sf_bessel_In_scaled_e($n, $x, $result)>
=item C<gsl_sf_bessel_In_scaled($n, $x)>
-These routines compute the scaled regular modified cylindrical Bessel function of order $n, \exp(-|x|) I_n(x)
=back
=over
=item C<gsl_sf_bessel_In_scaled_array>
-
=back
=over
=item C<gsl_sf_bessel_K0_e($x, $result)>
=item C<gsl_sf_bessel_K0($x)>
-These routines compute the irregular modified cylindrical Bessel function of zeroth order, K_0(x), for x > 0.
=back
=over
=item C<gsl_sf_bessel_K1_e($x, $result)>
=item C<gsl_sf_bessel_K1($x)>
-These routines compute the irregular modified cylindrical Bessel function of first order, K_1(x), for x > 0.
=back
=over
=item C<gsl_sf_bessel_Kn_e($n, $x, $result)>
=item C<gsl_sf_bessel_Kn($n, $x)>
-These routines compute the irregular modified cylindrical Bessel function of order $n, K_n(x), for x > 0.
=back
=over
=item C<gsl_sf_bessel_Kn_array>
-
=back
=over
=item C<gsl_sf_bessel_K0_scaled_e($x, $result)>
=item C<gsl_sf_bessel_K0_scaled($x)>
-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<gsl_sf_bessel_K1_scaled_e($x, $result)>
=item C<gsl_sf_bessel_K1_scaled($x)>
-
=back
=over
=item C<gsl_sf_bessel_Kn_scaled_e($n, $x, $result)>
=item C<gsl_sf_bessel_Kn_scaled($n, $x)>
-
=back
=over
=item C<gsl_sf_bessel_Kn_scaled_array >
-
=back
=over
=item C<gsl_sf_bessel_j0_e($x, $result)>
=item C<gsl_sf_bessel_j0($x)>
-
=back
=over
=item C<gsl_sf_bessel_j1_e($x, $result)>
=item C<gsl_sf_bessel_j1($x)>
-
=back
=over
=item C<gsl_sf_bessel_j2_e($x, $result)>
=item C<gsl_sf_bessel_j2($x)>
-
=back
=over
=item C<gsl_sf_bessel_jl_e($l, $x, $result)>
=item C<gsl_sf_bessel_jl($l, $x)>
-
=back
=over
=item C<gsl_sf_bessel_jl_array>
-
=back
=over
=item C<gsl_sf_bessel_jl_steed_array>
-
=back
=over
=item C<gsl_sf_bessel_y0_e($x, $result)>
=item C<gsl_sf_bessel_y0($x)>
-
=back
=over
=item C<gsl_sf_bessel_y1_e($x, $result)>
=item C<gsl_sf_bessel_y1($x)>
-
=back
=over
=item C<gsl_sf_bessel_y2_e($x, $result)>
=item C<gsl_sf_bessel_y2($x)>
-
=back
=over
=item C<gsl_sf_bessel_yl_e($l, $x, $result)>
=item C<gsl_sf_bessel_yl($l, $x)>
-
=back
=over
=item C<gsl_sf_bessel_yl_array>
-
=back
=over
=item C<gsl_sf_bessel_i0_scaled_e($x, $result)>
=item C<gsl_sf_bessel_i0_scaled($x)>
-
=back
=over
=item C<gsl_sf_bessel_i1_scaled_e($x, $result)>
=item C<gsl_sf_bessel_i1_scaled($x)>
-
=back
=over
=item C<gsl_sf_bessel_i2_scaled_e($x, $result)>
=item C<gsl_sf_bessel_i2_scaled($x)>
-
=back
=over
=item C<gsl_sf_bessel_il_scaled_e($l, $x, $result)>
=item C<gsl_sf_bessel_il_scaled($x)>
-
=back
=over
=item C<gsl_sf_bessel_il_scaled_array>
-
=back
=over
=item C<gsl_sf_bessel_k0_scaled_e($x, $result)>
=item C<gsl_sf_bessel_k0_scale($x)>
-
=back
=over
=item C<gsl_sf_bessel_k1_scaled_e($x, $result)>
=item C<gsl_sf_bessel_k1_scaled($x)>
-
=back
=over
=item C<gsl_sf_bessel_k2_scaled_e($x, $result) >
=item C<gsl_sf_bessel_k2_scaled($x)>
-
=back
=over
=item C<gsl_sf_bessel_kl_scaled_e($l, $x, $result)>
=item C<gsl_sf_bessel_kl_scaled($l, $x)>
-
=back
=over
=item C<gsl_sf_bessel_kl_scaled_array>
-
=back
=over
=item C<gsl_sf_bessel_Jnu_e($nu, $x, $result)>
=item C<gsl_sf_bessel_Jnu($nu, $x)>
-
=back
=over
=item C<gsl_sf_bessel_sequence_Jnu_e >
-
=back
=over
=item C<gsl_sf_bessel_Ynu_e($nu, $x, $result)>
=item C<gsl_sf_bessel_Ynu($nu, $x)>
-
=back
=over
=item C<gsl_sf_bessel_Inu_scaled_e($nu, $x, $result)>
=item C<gsl_sf_bessel_Inu_scaled($nu, $x)>
-
=back
=over
=item C<gsl_sf_bessel_Inu_e($nu, $x, $result)>
=item C<gsl_sf_bessel_Inu($nu, $x)>
-
=back
=over
=item C<gsl_sf_bessel_Knu_scaled_e($nu, $x, $result)>
=item C<gsl_sf_bessel_Knu_scaled($nu, $x)>
-
=back
=over
=item C<gsl_sf_bessel_Knu_e($nu, $x, $result)>
=item C<gsl_sf_bessel_Knu($nu, $x)>
-
=back
=over
=item C<gsl_sf_bessel_lnKnu_e($nu, $x, $result)>
=item C<gsl_sf_bessel_lnKnu($nu, $x)>
-
=back
=over
=item C<gsl_sf_bessel_zero_J0_e($s, $result)>
=item C<gsl_sf_bessel_zero_J0($s)>
-
=back
=over
=item C<gsl_sf_bessel_zero_J1_e($s, $result)>
=item C<gsl_sf_bessel_zero_J1($s)>
-
=back
=over
=item C<gsl_sf_bessel_zero_Jnu_e($nu, $s, $result)>
=item C<gsl_sf_bessel_zero_Jnu($nu, $s)>
-
=back
=over
=item C<gsl_sf_clausen_e($x, $result)>
=item C<gsl_sf_clausen($x)>
-
=back
=over
=item C<gsl_sf_hydrogenicR_1_e($Z, $r, $result)>
=item C<gsl_sf_hydrogenicR_1($Z, $r)>
-
=back
=over
=item C<gsl_sf_hydrogenicR_e($n, $l, $Z, $r, $result)>
=item C<gsl_sf_hydrogenicR($n, $l, $Z, $r)>
-
=back
=over
=item C<gsl_sf_coulomb_wave_FG_e($eta, $x, $L_F, $k, $F, gsl_sf_result * Fp, gsl_sf_result * G, $Gp)> - 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, $GSL_EOVRFLW is returned and scaling exponents are returned as second and third values.
=item C<gsl_sf_coulomb_wave_F_array > -
=item C<gsl_sf_coulomb_wave_FG_array> -
=item C<gsl_sf_coulomb_wave_FGp_array> -
=item C<gsl_sf_coulomb_wave_sphF_array> -
=item C<gsl_sf_coulomb_CL_e($L, $eta, $result)> - This function computes the Coulomb wave function normalization constant C_L($eta) for $L > -1.
=item C<gsl_sf_coulomb_CL_arrayi> -
=back
=over
=item C<gsl_sf_coupling_3j_e($two_ja, $two_jb, $two_jc, $two_ma, $two_mb, $two_mc, $result)>
=item C<gsl_sf_coupling_3j($two_ja, $two_jb, $two_jc, $two_ma, $two_mb, $two_mc)>
- 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 = $two_ma/2, etc.
=back
=over
=item C<gsl_sf_coupling_6j_e($two_ja, $two_jb, $two_jc, $two_jd, $two_je, $two_jf, $result)>
=item C<gsl_sf_coupling_6j($two_ja, $two_jb, $two_jc, $two_jd, $two_je, $two_jf)>
- 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 = $two_ma/2, etc.
=back
=over
=item C<gsl_sf_coupling_RacahW_e>
=item C<gsl_sf_coupling_RacahW>
-
=back
=over
=item C<gsl_sf_coupling_9j_e($two_ja, $two_jb, $two_jc, $two_jd, $two_je, $two_jf, $two_jg, $two_jh, $two_ji, $result)>
=item C<gsl_sf_coupling_9j($two_ja, $two_jb, $two_jc, $two_jd, $two_je, $two_jf, $two_jg, $two_jh, $two_ji)>
-These routines compute the Wigner 9-j coefficient,
{ja jb jc
jd je jf
jg jh ji}
where the arguments are given in half-integer units, ja = two_ja/2, ma = two_ma/2, etc.
=back
=over
=item C<gsl_sf_dawson_e($x, $result)>
=item C<gsl_sf_dawson($x)>
-These routines compute the value of Dawson's integral for $x.
=back
=over
=item C<gsl_sf_debye_1_e($x, $result)>
=item C<gsl_sf_debye_1($x)>
-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<gsl_sf_debye_2_e($x, $result)>
=item C<gsl_sf_debye_2($x)>
-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<gsl_sf_debye_3_e($x, $result)>
=item C<gsl_sf_debye_3($x)>
-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<gsl_sf_debye_4_e($x, $result)>
=item C<gsl_sf_debye_4($x)>
-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<gsl_sf_debye_5_e($x, $result)>
=item C<gsl_sf_debye_5($x)>
-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<gsl_sf_debye_6_e($x, $result)>
=item C<gsl_sf_debye_6($x)>
-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<gsl_sf_dilog_e ($x, $result)>
=item C<gsl_sf_dilog($x)>
- 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<gsl_sf_complex_dilog_xy_e> -
=item C<gsl_sf_complex_dilog_e($r, $theta, $result_re, $result_im)> - 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 $result_im gsl_result structs.
=item C<gsl_sf_complex_spence_xy_e> -
=back
=over
=item C<gsl_sf_multiply>
=item C<gsl_sf_multiply_e($x, $y, $result)> - This function multiplies $x and $y storing the product and its associated error in $result.
=item C<gsl_sf_multiply_err_e($x, $dx, $y, $dy, $result)> - 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 $result.
-
=back
=over
=item C<gsl_sf_ellint_Kcomp_e($k, $mode, $result)>
=item C<gsl_sf_ellint_Kcomp($k, $mode)>
-These routines compute the complete elliptic integral K($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<gsl_sf_ellint_Ecomp_e($k, $mode, $result)>
=item C<gsl_sf_ellint_Ecomp($k, $mode)>
-
=back
=over
=item C<gsl_sf_ellint_Pcomp_e($k, $n, $mode, $result)>
=item C<gsl_sf_ellint_Pcomp($k, $n, $mode)>
-
=back
=over
=item C<gsl_sf_ellint_Dcomp_e>
=item C<gsl_sf_ellint_Dcomp >
-
=back
=over
=item C<gsl_sf_ellint_F_e($phi, $k, $mode, $result)>
=item C<gsl_sf_ellint_F($phi, $k, $mode)>
-These routines compute the incomplete elliptic integral F($phi,$k) to the accuracy specified by the mode variable mode. Note that Abramowitz & Stegun define this function in terms of the parameter m = k^2.
=back
=over
=item C<gsl_sf_ellint_E_e($phi, $k, $mode, $result)>
=item C<gsl_sf_ellint_E($phi, $k, $mode)>
-These routines compute the incomplete elliptic integral E($phi,$k) to the accuracy specified by the mode variable mode. Note that Abramowitz & Stegun define this function in terms of the parameter m = k^2.
=back
=over
=item C<gsl_sf_ellint_P_e($phi, $k, $n, $mode, $result)>
=item C<gsl_sf_ellint_P($phi, $k, $n, $mode)>
-These routines compute the incomplete elliptic integral \Pi(\phi,k,n) to the accuracy specified by the mode variable mode. Note that Abramowitz & Stegun define this function in terms of the parameters m = k^2 and \sin^2(\alpha) = k^2, with the change of sign n \to -n.
=back
=over
=item C<gsl_sf_ellint_D_e($phi, $k, $n, $mode, $result)>
=item C<gsl_sf_ellint_D($phi, $k, $n, $mode)>
-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 $n is not used and will be removed in a future release.
=back
=over
=item C<gsl_sf_ellint_RC_e($x, $y, $mode, $result)>
=item C<gsl_sf_ellint_RC($x, $y, $mode)>
- These routines compute the incomplete elliptic integral RC($x,$y) to the accuracy specified by the mode variable $mode.
=back
=over
=item C<gsl_sf_ellint_RD_e($x, $y, $z, $mode, $result)>
=item C<gsl_sf_ellint_RD($x, $y, $z, $mode)>
- These routines compute the incomplete elliptic integral RD($x,$y,$z) to the accuracy specified by the mode variable $mode.
=back
=over
=item C<gsl_sf_ellint_RF_e($x, $y, $z, $mode, $result)>
=item C<gsl_sf_ellint_RF($x, $y, $z, $mode)>
- These routines compute the incomplete elliptic integral RF($x,$y,$z) to the accuracy specified by the mode variable $mode.
=back
=over
=item C<gsl_sf_ellint_RJ_e($x, $y, $z, $p, $mode, $result)>
=item C<gsl_sf_ellint_RJ($x, $y, $z, $p, $mode)>
- These routines compute the incomplete elliptic integral RJ($x,$y,$z,$p) to the accuracy specified by the mode variable $mode.
=back
=over
=item C<gsl_sf_elljac_e($u, $m)> - This function computes the Jacobian elliptic functions sn(u|m), cn(u|m), dn(u|m) by descending Landen transformations. The function returns 0 if the operation succeded, 1 otherwise and then returns the result of sn, cn and dn in this order.
=item C<gsl_sf_erfc_e($x, $result)>
=item C<gsl_sf_erfc($x)>
-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<gsl_sf_log_erfc_e($x, $result)>
=item C<gsl_sf_log_erfc($x)>
-These routines compute the logarithm of the complementary error function \log(\erfc(x)).
=back
=over
=item C<gsl_sf_erf_e($x, $result)>
=item C<gsl_sf_erf($x)>
-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<gsl_sf_erf_Z_e($x, $result)>
=item C<gsl_sf_erf_Z($x)>
-These routines compute the Gaussian probability density function Z(x) = (1/\sqrt{2\pi}) \exp(-x^2/2).
=back
=over
=item C<gsl_sf_erf_Q_e($x, $result)>
=item C<gsl_sf_erf_Q($x)>
- 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<gsl_sf_hazard_e($x, $result)>
=item C<gsl_sf_hazard($x)>
- These routines compute the hazard function for the normal distribution.
=back
=over
=item C<gsl_sf_exp_e($x, $result)>
=item C<gsl_sf_exp($x)>
- These routines provide an exponential function \exp(x) using GSL semantics and error checking.
=back
=over
=item C<gsl_sf_exp_e10_e> -
=back
=over
=item C<gsl_sf_exp_mult_e >
=item C<gsl_sf_exp_mult>
-
=back
=over
=item C<gsl_sf_exp_mult_e10_e> -
=back
=over
=item C<gsl_sf_expm1_e($x, $result)>
=item C<gsl_sf_expm1($x)>
-These routines compute the quantity \exp(x)-1 using an algorithm that is accurate for small x.
=back
=over
=item C<gsl_sf_exprel_e($x, $result)>
=item C<gsl_sf_exprel($x)>
-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<gsl_sf_exprel_2_e($x, $result)>
=item C<gsl_sf_exprel_2($x)>
-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<gsl_sf_exprel_n_e($x, $result)>
=item C<gsl_sf_exprel_n($x)>
-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<gsl_sf_exp_err_e($x, $dx, $result)> - This function exponentiates $x with an associated absolute error $dx.
=item C<gsl_sf_exp_err_e10_e> -
=item C<gsl_sf_exp_mult_err_e($x, $dx, $y, $dy, $result)> -
=item C<gsl_sf_exp_mult_err_e10_e> -
=back
=over
=item C<gsl_sf_expint_E1_e($x, $result)>
=item C<gsl_sf_expint_E1($x)>
-These routines compute the exponential integral E_1(x), E_1(x) := \Re \int_1^\infty dt \exp(-xt)/t.
=back
=over
=item C<gsl_sf_expint_E2_e($x, $result)>
=item C<gsl_sf_expint_E2($x)>
-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<gsl_sf_expint_En_e($n, $x, $result)>
=item C<gsl_sf_expint_En($n, $x)>
-These routines compute the exponential integral E_n(x) of order n,
E_n(x) := \Re \int_1^\infty dt \exp(-xt)/t^n.
=back
=over
=item C<gsl_sf_expint_E1_scaled_e >
=item C<gsl_sf_expint_E1_scaled>
-
=back
=over
=item C<gsl_sf_expint_E2_scaled_e>
=item C<gsl_sf_expint_E2_scaled >
-
=back
=over
=item C<gsl_sf_expint_En_scaled_e>
=item C<gsl_sf_expint_En_scaled>
-
=back
=over
=item C<gsl_sf_expint_Ei_e($x, $result)>
=item C<gsl_sf_expint_Ei($x)>
-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<gsl_sf_expint_Ei_scaled_e>
=item C<gsl_sf_expint_Ei_scaled >
-
=back
=over
=item C<gsl_sf_Shi_e($x, $result)>
=item C<gsl_sf_Shi($x)>
-These routines compute the integral Shi(x) = \int_0^x dt \sinh(t)/t.
=back
=over
=item C<gsl_sf_Chi_e($x, $result)>
=item C<gsl_sf_Chi($x)>
-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 $M_EULER from the Math::GSL::Const module).
=back
=over
=item C<gsl_sf_expint_3_e($x, $result)>
=item C<gsl_sf_expint_3($x)>
-These routines compute the third-order exponential integral Ei_3(x) = \int_0^xdt \exp(-t^3) for x >= 0.
=back
=over
=item C<gsl_sf_Si_e($x, $result)>
=item C<gsl_sf_Si($x)>
-These routines compute the Sine integral Si(x) = \int_0^x dt \sin(t)/t.
=back
=over
=item C<gsl_sf_Ci_e($x, $result)>
=item C<gsl_sf_Ci($x)>
-These routines compute the Cosine integral Ci(x) = -\int_x^\infty dt \cos(t)/t for x > 0.
=back
=over
=item C<gsl_sf_fermi_dirac_m1_e($x, $result)>
=item C<gsl_sf_fermi_dirac_m1($x)>
-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<gsl_sf_fermi_dirac_0_e($x, $result)>
=item C<gsl_sf_fermi_dirac_0($x)>
-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<gsl_sf_fermi_dirac_1_e($x, $result)>
=item C<gsl_sf_fermi_dirac_1($x)>
-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<gsl_sf_fermi_dirac_2_e($x, $result)>
=item C<gsl_sf_fermi_dirac_2($x)>
-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<gsl_sf_fermi_dirac_int_e($j, $x, $result)>
=item C<gsl_sf_fermi_dirac_int($j, $x)>
-These routines compute the complete Fermi-Dirac integral with an integer index of j, F_j(x) = (1/\Gamma(j+1)) \int_0^\infty dt (t^j /(\exp(t-x)+1)).
=back
=over
=item C<gsl_sf_fermi_dirac_mhalf_e($x, $result)>
=item C<gsl_sf_fermi_dirac_mhalf($x)>
-These routines compute the complete Fermi-Dirac integral F_{-1/2}(x).
=back
=over
=item C<gsl_sf_fermi_dirac_half_e($x, $result)>
=item C<gsl_sf_fermi_dirac_half($x)>
-These routines compute the complete Fermi-Dirac integral F_{1/2}(x).
=back
=over
=item C<gsl_sf_fermi_dirac_3half_e($x, $result)>
=item C<gsl_sf_fermi_dirac_3half($x)>
-These routines compute the complete Fermi-Dirac integral F_{3/2}(x).
=back
=over
=item C<gsl_sf_fermi_dirac_inc_0_e($x, $b, $result)>
=item C<gsl_sf_fermi_dirac_inc_0($x, $b, $result)>
-These routines compute the incomplete Fermi-Dirac integral with an index of zero, F_0(x,b) = \ln(1 + e^{b-x}) - (b-x).
=back
=over
=item C<gsl_sf_legendre_Pl_e($l, $x, $result)>
=item C<gsl_sf_legendre_Pl($l, $x)>
-These functions evaluate the Legendre polynomial P_l(x) for a specific value of l, x subject to l >= 0, |x| <= 1
=back
=over
=item C<gsl_sf_legendre_Pl_array>
=item C<gsl_sf_legendre_Pl_deriv_array>
-
=back
=over
=item C<gsl_sf_legendre_P1_e($x, $result)>
=item C<gsl_sf_legendre_P2_e($x, $result)>
=item C<gsl_sf_legendre_P3_e($x, $result)>
=item C<gsl_sf_legendre_P1($x)>
=item C<gsl_sf_legendre_P2($x)>
=item C<gsl_sf_legendre_P3($x)>
-These functions evaluate the Legendre polynomials P_l(x) using explicit representations for l=1, 2, 3.
=back
=over
=item C<gsl_sf_legendre_Q0_e($x, $result)>
=item C<gsl_sf_legendre_Q0($x)>
-These routines compute the Legendre function Q_0(x) for x > -1, x != 1.
=back
=over
=item C<gsl_sf_legendre_Q1_e($x, $result)>
=item C<gsl_sf_legendre_Q1($x)>
-These routines compute the Legendre function Q_1(x) for x > -1, x != 1.
=back
=over
=item C<gsl_sf_legendre_Ql_e($l, $x, $result)>
=item C<gsl_sf_legendre_Ql($l, $x)>
-These routines compute the Legendre function Q_l(x) for x > -1, x != 1 and l >= 0.
=back
=over
=item C<gsl_sf_legendre_Plm_e($l, $m, $x, $result)>
=item C<gsl_sf_legendre_Plm($l, $m, $x)>
-These routines compute the associated Legendre polynomial P_l^m(x) for m >= 0, l >= m, |x| <= 1.
=back
=over
=item C<gsl_sf_legendre_Plm_array>
=item C<gsl_sf_legendre_Plm_deriv_array >
-
=back
=over
=item C<gsl_sf_legendre_sphPlm_e($l, $m, $x, $result)>
=item C<gsl_sf_legendre_sphPlm($l, $m, $x)>
-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<gsl_sf_legendre_sphPlm_array >
=item C<gsl_sf_legendre_sphPlm_deriv_array>
-
=back
=over
=item C<gsl_sf_legendre_array_size> -
=back
=over
=item C<gsl_sf_lngamma_e($x, $result)>
=item C<gsl_sf_lngamma($x)>
-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<gsl_sf_lngamma_sgn_e($x, $result_lg)> - 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<gsl_sf_gamma_e >
=item C<gsl_sf_gamma>
-
=back
=over
=item C<gsl_sf_gammastar_e>
=item C<gsl_sf_gammastar >
-
=back
=over
=item C<gsl_sf_gammainv_e>
=item C<gsl_sf_gammainv>
-
=back
=over
=item C<gsl_sf_lngamma_complex_e >
-
=back
=over
=item C<gsl_sf_gamma_inc_Q_e>
=item C<gsl_sf_gamma_inc_Q>
-
=back
=over
=item C<gsl_sf_gamma_inc_P_e >
=item C<gsl_sf_gamma_inc_P>
-
=back
=over
=item C<gsl_sf_gamma_inc_e>
=item C<gsl_sf_gamma_inc >
-
=back
=over
=item C<gsl_sf_taylorcoeff_e>
=item C<gsl_sf_taylorcoeff>
-
=back
=over
=item C<gsl_sf_fact_e >
=item C<gsl_sf_fact>
-
=back
=over
=item C<gsl_sf_doublefact_e>
=item C<gsl_sf_doublefact >
-
=back
=over
=item C<gsl_sf_lnfact_e>
=item C<gsl_sf_lnfact>
-
=back
=over
=item C<gsl_sf_lndoublefact_e >
=item C<gsl_sf_lndoublefact>
-
=back
=over
=item C<gsl_sf_lnchoose_e>
=item C<gsl_sf_lnchoose >
-
=back
=over
=item C<gsl_sf_choose_e>
=item C<gsl_sf_choose>
-
=back
=over
=item C<gsl_sf_lnpoch_e >
=item C<gsl_sf_lnpoch>
-
=back
=over
=item C<gsl_sf_lnpoch_sgn_e>
-
=back
=over
=item C<gsl_sf_poch_e >
=item C<gsl_sf_poch>
-
=back
=over
=item C<gsl_sf_pochrel_e>
=item C<gsl_sf_pochrel >
-
=back
=over
=item C<gsl_sf_lnbeta_e>
=item C<gsl_sf_lnbeta>
-
=back
=over
=item C<gsl_sf_lnbeta_sgn_e >
-
=back
=over
=item C<gsl_sf_beta_e>
=item C<gsl_sf_beta>
-
=back
=over
=item C<gsl_sf_beta_inc_e >
=item C<gsl_sf_beta_inc>
-
=back
=over
=item C<gsl_sf_gegenpoly_1_e>
=item C<gsl_sf_gegenpoly_2_e >
=item C<gsl_sf_gegenpoly_3_e>
=item C<gsl_sf_gegenpoly_1>
=item C<gsl_sf_gegenpoly_2 >
=item C<gsl_sf_gegenpoly_3>
-
=back
=over
=item C<gsl_sf_gegenpoly_n_e>
=item C<gsl_sf_gegenpoly_n >
-
=back
=over
=item C<gsl_sf_gegenpoly_array>
=item C<gsl_sf_hyperg_0F1_e>
=item C<gsl_sf_hyperg_0F1 >
-
=back
=over
=item C<gsl_sf_hyperg_1F1_int_e>
=item C<gsl_sf_hyperg_1F1_int>
-
=back
=over
=item C<gsl_sf_hyperg_1F1_e >
=item C<gsl_sf_hyperg_1F1>
-
=back
=over
=item C<gsl_sf_hyperg_U_int_e>
=item C<gsl_sf_hyperg_U_int >
-
=back
=over
=item C<gsl_sf_hyperg_U_int_e10_e>
-
=back
=over
=item C<gsl_sf_hyperg_U_e>
=item C<gsl_sf_hyperg_U >
-
=back
=over
=item C<gsl_sf_hyperg_U_e10_e>
-
=back
=over
=item C<gsl_sf_hyperg_2F1_e>
=item C<gsl_sf_hyperg_2F1 >
-
=back
=over
=item C<gsl_sf_hyperg_2F1_conj_e>
=item C<gsl_sf_hyperg_2F1_conj>
-
=back
=over
=item C<gsl_sf_hyperg_2F1_renorm_e >
=item C<gsl_sf_hyperg_2F1_renorm>
-
=back
=over
=item C<gsl_sf_hyperg_2F1_conj_renorm_e>
=item C<gsl_sf_hyperg_2F1_conj_renorm >
-
=back
=over
=item C<gsl_sf_hyperg_2F0_e>
=item C<gsl_sf_hyperg_2F0>
-
=back
=over
=item C<gsl_sf_laguerre_1_e >
=item C<gsl_sf_laguerre_2_e>
=item C<gsl_sf_laguerre_3_e>
=item C<gsl_sf_laguerre_1 >
=item C<gsl_sf_laguerre_2>
=item C<gsl_sf_laguerre_3>
-
=back
=over
=item C<gsl_sf_laguerre_n_e >
=item C<gsl_sf_laguerre_n>
-
=back
=over
=item C<gsl_sf_lambert_W0_e>
=item C<gsl_sf_lambert_W0 >
-
=back
=over
=item C<gsl_sf_lambert_Wm1_e>
=item C<gsl_sf_lambert_Wm1>
-
=back
=over
=item C<gsl_sf_conicalP_half_e >
=item C<gsl_sf_conicalP_half>
-
=back
=over
=item C<gsl_sf_conicalP_mhalf_e>
=item C<gsl_sf_conicalP_mhalf >
-
=back
=over
=item C<gsl_sf_conicalP_0_e>
=item C<gsl_sf_conicalP_0>
-
=back
=over
=item C<gsl_sf_conicalP_1_e >
=item C<gsl_sf_conicalP_1>
-
=back
=over
=item C<gsl_sf_conicalP_sph_reg_e>
=item C<gsl_sf_conicalP_sph_reg >
-
=back
=over
=item C<gsl_sf_conicalP_cyl_reg_e>
=item C<gsl_sf_conicalP_cyl_reg>
-
=back
=over
=item C<gsl_sf_legendre_H3d_0_e >
=item C<gsl_sf_legendre_H3d_0>
-
=back
=over
=item C<gsl_sf_legendre_H3d_1_e>
=item C<gsl_sf_legendre_H3d_1 >
-
=back
=over
=item C<gsl_sf_legendre_H3d_e>
=item C<gsl_sf_legendre_H3d>
-
=back
=over
=item C<gsl_sf_legendre_H3d_array >
-
=back
=over
=item C<gsl_sf_log_e>
=item C<gsl_sf_log>
-
=back
=over
=item C<gsl_sf_log_abs_e >
=item C<gsl_sf_log_abs>
-
=back
=over
=item C<gsl_sf_complex_log_e>
-
=back
=over
=item C<gsl_sf_log_1plusx_e >
=item C<gsl_sf_log_1plusx>
-
=back
=over
=item C<gsl_sf_log_1plusx_mx_e>
=item C<gsl_sf_log_1plusx_mx >
-
=back
=over
=item C<gsl_sf_mathieu_a_array>
=item C<gsl_sf_mathieu_b_array>
-
=back
=over
=item C<gsl_sf_mathieu_a >
=item C<gsl_sf_mathieu_b>
-
=back
=over
=item C<gsl_sf_mathieu_a_coeff>
=item C<gsl_sf_mathieu_b_coeff >
-
=back
=over
=item C<gsl_sf_mathieu_alloc>
-
=back
=over
=item C<gsl_sf_mathieu_free>
-
=back
=over
=item C<gsl_sf_mathieu_ce >
=item C<gsl_sf_mathieu_se>
-
=back
=over
=item C<gsl_sf_mathieu_ce_array>
=item C<gsl_sf_mathieu_se_array >
-
=back
=over
=item C<gsl_sf_mathieu_Mc>
=item C<gsl_sf_mathieu_Ms>
-
=back
=over
=item C<gsl_sf_mathieu_Mc_array >
=item C<gsl_sf_mathieu_Ms_array>
-
=back
=over
=item C<gsl_sf_pow_int_e>
=item C<gsl_sf_pow_int >
-
=back
=over
=item C<gsl_sf_psi_int_e>
=item C<gsl_sf_psi_int>
-
=back
=over
=item C<gsl_sf_psi_e >
=item C<gsl_sf_psi>
-
=back
=over
=item C<gsl_sf_psi_1piy_e>
=item C<gsl_sf_psi_1piy >
-
=back
=over
=item C<gsl_sf_complex_psi_e>
-
=back
=over
=item C<gsl_sf_psi_1_int_e>
=item C<gsl_sf_psi_1_int >
-
=back
=over
=item C<gsl_sf_psi_1_e >
=item C<gsl_sf_psi_1>
-
=back
=over
=item C<gsl_sf_psi_n_e >
=item C<gsl_sf_psi_n>
-
=back
=over
=item C<gsl_sf_result_smash_e>
-
=back
=over
=item C<gsl_sf_synchrotron_1_e >
=item C<gsl_sf_synchrotron_1>
-
=back
=over
=item C<gsl_sf_synchrotron_2_e>
=item C<gsl_sf_synchrotron_2 >
-
=back
=over
=item C<gsl_sf_transport_2_e>
=item C<gsl_sf_transport_2>
-
=back
=over
=item C<gsl_sf_transport_3_e >
=item C<gsl_sf_transport_3>
-
=back
=over
=item C<gsl_sf_transport_4_e>
=item C<gsl_sf_transport_4 >
-
=back
=over
=item C<gsl_sf_transport_5_e>
=item C<gsl_sf_transport_5>
-
=back
=over
=item C<gsl_sf_sin_e >
=item C<gsl_sf_sin>
-
=back
=over
=item C<gsl_sf_cos_e>
=item C<gsl_sf_cos >
-
=back
=over
=item C<gsl_sf_hypot_e>
=item C<gsl_sf_hypot>
-
=back
=over
=item C<gsl_sf_complex_sin_e >
-
=back
=over
=item C<gsl_sf_complex_cos_e>
-
=back
=over
=item C<gsl_sf_complex_logsin_e>
-
=back
=over
=item C<gsl_sf_sinc_e >
=item C<gsl_sf_sinc>
-
=back
=over
=item C<gsl_sf_lnsinh_e>
=item C<gsl_sf_lnsinh >
-
=back
=over
=item C<gsl_sf_lncosh_e>
=item C<gsl_sf_lncosh>
-
=back
=over
=item C<gsl_sf_polar_to_rect >
-
=back
=over
=item C<gsl_sf_rect_to_polar>
-
=back
=over
=item C<gsl_sf_sin_err_e>
=item C<gsl_sf_cos_err_e >
-
=back
=over
=item C<gsl_sf_angle_restrict_symm_e>
=item C<gsl_sf_angle_restrict_symm>
-
=back
=over
=item C<gsl_sf_angle_restrict_pos_e >
=item C<gsl_sf_angle_restrict_pos>
-
=back
=over
=item C<gsl_sf_angle_restrict_symm_err_e>
=item C<gsl_sf_angle_restrict_pos_err_e >
=over
=item C<gsl_sf_atanint_e>
=item C<gsl_sf_atanint>
-These routines compute the Arctangent integral, which is defined as AtanInt(x) = \int_0^x dt \arctan(t)/t.
=back
=item C<gsl_sf_zeta_int_e >
=item C<gsl_sf_zeta_int>
=item C<gsl_sf_zeta_e gsl_sf_zeta >
=item C<gsl_sf_zetam1_e>
=item C<gsl_sf_zetam1>
=item C<gsl_sf_zetam1_int_e >
=item C<gsl_sf_zetam1_int>
=item C<gsl_sf_hzeta_e>
=item C<gsl_sf_hzeta >
=item C<gsl_sf_eta_int_e>
=item C<gsl_sf_eta_int>
=item C<gsl_sf_eta_e>
=item C<gsl_sf_eta >
=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 avaible 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<airy>
=item C<bessel>
=item C<clausen>
=item C<hydrogenic>
=item C<coulumb>
=item C<coupling>
=item C<dawson>
=item C<debye>
=item C<dilog>
=item C<factorial>
=item C<misc>
=item C<elliptic>
=item C<error>
=item C<hypergeometric>
=item C<laguerre>
=item C<legendre>
=item C<gamma>
=item C<transport>
=item C<trig>
=item C<zeta>
=item C<eta>
=item C<vars>
=back
For more informations on the functions, we refer you to the GSL offcial
documentation: L<http://www.gnu.org/software/gsl/manual/html_node/>
Tip : search on google: site:http://www.gnu.org/software/gsl/manual/html_node/name_of_the_function_you_want
=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<examples/sf> folder of the source code.
=head1 AUTHORS
Jonathan Leto <jonathan@leto.net> and Thierry Moisan <thierry.moisan@gmail.com>
=head1 COPYRIGHT AND LICENSE
Copyright (C) 2008-2009 Jonathan 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
%}