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SF.pod
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SF.pod
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%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)>