/
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__
=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 = $r->{err};
Here is a list of all included functions:
=over
=item C<gsl_sf_airy_Ai_e($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, $x)>
This routine computes the values of the regular cylindrical Bessel functions
J_n($x) for n from $nmin to $nmax inclusive, returning the results in an array
reference. The values are computed using recurrence relations for
efficiency, and therefore may differ slightly from the exact values.
=back
=over
=item C<gsl_sf_bessel_Y0_e($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 $n, Y_n(x), for x>0.
=back
=over
=item C<gsl_sf_bessel_Yn_array($nmin, $nmax, $x)>
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 $x>0. The values are computed using
recurrence relations for efficiency, and therefore may differ slightly from the
exact values.
=back
=over
=item C<gsl_sf_bessel_I0_e($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)>
=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 $n, I_n(x).
=back
=over
=item C<gsl_sf_bessel_In_array($nmin, $nmax, $x)>
This routine computes the values of the regular modified cylindrical Bessel
functions I_n(x) for n from $nmin to $nmax inclusive, returning the results in an
array reference. The start of the range nmin must be positive or zero. The
values are computed using recurrence relations for efficiency, and therefore may
differ slightly from the exact values.
=back
=over
=item C<gsl_sf_bessel_I0_scaled_e($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 $n, \exp(-|x|) I_n(x)
=back
=over
=item C<gsl_sf_bessel_In_scaled_array($nmin, $nmax, $x)>
This routine computes the values of the scaled regular cylindrical Bessel
functions exp(-|$x|) I_n($x) for n from $nmin to $nmax inclusive, returning the
results in an array reference. The start of the range nmin must be positive
or zero. The values are computed using recurrence relations for efficiency, and
therefore may differ slightly from the exact values.
=back
=over
=item C<gsl_sf_bessel_K0_e($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 $n, K_n(x), for x > 0.
=back
=over
=item C<gsl_sf_bessel_Kn_array($nmin, $nmax, $x)>
This routine computes the values of the Irregular Modified Cylindrical Bessel Functions
K_n($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 $x and with throw an exception otherwise.
=back
=over
=item C<gsl_sf_bessel_K0_scaled_e($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, $x)>
=back
=over
=item C<gsl_sf_bessel_Kn_scaled_array($nmin, $max, $x) >
This routine computes the values of the scaled irregular cylindrical Bessel
functions exp(x) K_n(x) for n from nmin to nmax inclusive, storing the results
in the array result_array. The start of the range nmin must be positive or zero.
The domain of the function is x>0. The values are computed using recurrence
relations for efficiency, and therefore may differ slightly from the exact
values.
=back
=over
=item C<gsl_sf_bessel_j0_e($x, $result)>
=item C<gsl_sf_bessel_j0($x)>
=back