NAME

Math::GSL::SF - Special Functions

SYNOPSIS

    use Math::GSL::SF qw /:all/;

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:

gsl_sf_airy_Ai_e($x, $mode)

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.

gsl_sf_airy_Bi_e($x, $mode, $result)

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.

gsl_sf_airy_Ai_scaled_e($x, $mode, $result)

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.

gsl_sf_airy_Bi_scaled_e($x, $mode, $result)

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.

gsl_sf_airy_Ai_deriv_e($x, $mode, $result)

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.

gsl_sf_airy_Bi_deriv_e($x, $mode, $result)

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.

gsl_sf_airy_Ai_deriv_scaled_e($x, $mode, $result)

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.

gsl_sf_airy_Bi_deriv_scaled_e($x, $mode, $result)

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.

gsl_sf_airy_zero_Ai_e($s, $result)

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.

gsl_sf_airy_zero_Bi_e($s, $result)

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.

gsl_sf_airy_zero_Ai_deriv_e($s, $result)

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.

gsl_sf_airy_zero_Bi_deriv_e($s, $result)

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.

gsl_sf_bessel_J0_e($x, $result)

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.

gsl_sf_bessel_J1_e($x, $result)

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.

gsl_sf_bessel_Jn_e($n, $x, $result)

gsl_sf_bessel_Jn($n, $x)

-These routines compute the regular cylindrical Bessel function of order n, J_n($x).

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.

gsl_sf_bessel_Y0_e($x, $result)

gsl_sf_bessel_Y0($x)

- These routines compute the irregular spherical Bessel function of zeroth order, y_0(x) = -\cos(x)/x.

gsl_sf_bessel_Y1_e($x, $result)

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.

gsl_sf_bessel_Yn_e($n, $x, $result)

gsl_sf_bessel_Yn($n, $x)

-These routines compute the irregular cylindrical Bessel function of order $n, Y_n(x), for x>0.

gsl_sf_bessel_Yn_array

-

gsl_sf_bessel_I0_e($x, $result)

gsl_sf_bessel_I0($x)

-These routines compute the regular modified cylindrical Bessel function of zeroth order, I_0(x).

gsl_sf_bessel_I1_e($x, $result)

gsl_sf_bessel_I1($x)

-These routines compute the regular modified cylindrical Bessel function of first order, I_1(x).

gsl_sf_bessel_In_e($n, $x, $result)

gsl_sf_bessel_In($n, $x)

-These routines compute the regular modified cylindrical Bessel function of order $n, I_n(x).

gsl_sf_bessel_In_array

-

gsl_sf_bessel_I0_scaled_e($x, $result)

gsl_sf_bessel_I0_scaled($x)

-These routines compute the scaled regular modified cylindrical Bessel function of zeroth order \exp(-|x|) I_0(x).

gsl_sf_bessel_I1_scaled_e($x, $result)

gsl_sf_bessel_I1_scaled($x)

-These routines compute the scaled regular modified cylindrical Bessel function of first order \exp(-|x|) I_1(x).

gsl_sf_bessel_In_scaled_e($n, $x, $result)

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)

gsl_sf_bessel_In_scaled_array

-

gsl_sf_bessel_K0_e($x, $result)

gsl_sf_bessel_K0($x)

-These routines compute the irregular modified cylindrical Bessel function of zeroth order, K_0(x), for x > 0.

gsl_sf_bessel_K1_e($x, $result)

gsl_sf_bessel_K1($x)

-These routines compute the irregular modified cylindrical Bessel function of first order, K_1(x), for x > 0.

gsl_sf_bessel_Kn_e($n, $x, $result)

gsl_sf_bessel_Kn($n, $x)

-These routines compute the irregular modified cylindrical Bessel function of order $n, K_n(x), for x > 0.

gsl_sf_bessel_Kn_array

-

gsl_sf_bessel_K0_scaled_e($x, $result)

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.

gsl_sf_bessel_K1_scaled_e($x, $result)

gsl_sf_bessel_K1_scaled($x)

-

gsl_sf_bessel_Kn_scaled_e($n, $x, $result)

gsl_sf_bessel_Kn_scaled($n, $x)

-

gsl_sf_bessel_Kn_scaled_array

-

gsl_sf_bessel_j0_e($x, $result)

gsl_sf_bessel_j0($x)

-

gsl_sf_bessel_j1_e($x, $result)

gsl_sf_bessel_j1($x)

-

gsl_sf_bessel_j2_e($x, $result)

gsl_sf_bessel_j2($x)

-

gsl_sf_bessel_jl_e($l, $x, $result)

gsl_sf_bessel_jl($l, $x)

-

gsl_sf_bessel_jl_array

-

gsl_sf_bessel_jl_steed_array

-

gsl_sf_bessel_y0_e($x, $result)

gsl_sf_bessel_y0($x)

-

gsl_sf_bessel_y1_e($x, $result)

gsl_sf_bessel_y1($x)

-

gsl_sf_bessel_y2_e($x, $result)

gsl_sf_bessel_y2($x)

-

gsl_sf_bessel_yl_e($l, $x, $result)

gsl_sf_bessel_yl($l, $x)

-

gsl_sf_bessel_yl_array

-

gsl_sf_bessel_i0_scaled_e($x, $result)

gsl_sf_bessel_i0_scaled($x)

-

gsl_sf_bessel_i1_scaled_e($x, $result)

gsl_sf_bessel_i1_scaled($x)

-

gsl_sf_bessel_i2_scaled_e($x, $result)

gsl_sf_bessel_i2_scaled($x)

-

gsl_sf_bessel_il_scaled_e($l, $x, $result)

gsl_sf_bessel_il_scaled($x)

-

gsl_sf_bessel_il_scaled_array

-

gsl_sf_bessel_k0_scaled_e($x, $result)

gsl_sf_bessel_k0_scale($x)

-

gsl_sf_bessel_k1_scaled_e($x, $result)

gsl_sf_bessel_k1_scaled($x)

-

gsl_sf_bessel_k2_scaled_e($x, $result)

gsl_sf_bessel_k2_scaled($x)

-

gsl_sf_bessel_kl_scaled_e($l, $x, $result)

gsl_sf_bessel_kl_scaled($l, $x)

-

gsl_sf_bessel_kl_scaled_array

-

gsl_sf_bessel_Jnu_e($nu, $x, $result)

gsl_sf_bessel_Jnu($nu, $x)

-

gsl_sf_bessel_sequence_Jnu_e

-

gsl_sf_bessel_Ynu_e($nu, $x, $result)

gsl_sf_bessel_Ynu($nu, $x)

-

gsl_sf_bessel_Inu_scaled_e($nu, $x, $result)

gsl_sf_bessel_Inu_scaled($nu, $x)

-

gsl_sf_bessel_Inu_e($nu, $x, $result)

gsl_sf_bessel_Inu($nu, $x)

-

gsl_sf_bessel_Knu_scaled_e($nu, $x, $result)

gsl_sf_bessel_Knu_scaled($nu, $x)

-

gsl_sf_bessel_Knu_e($nu, $x, $result)

gsl_sf_bessel_Knu($nu, $x)

-

gsl_sf_bessel_lnKnu_e($nu, $x, $result)

gsl_sf_bessel_lnKnu($nu, $x)

-

gsl_sf_bessel_zero_J0_e($s, $result)

gsl_sf_bessel_zero_J0($s)

-

gsl_sf_bessel_zero_J1_e($s, $result)

gsl_sf_bessel_zero_J1($s)

-

gsl_sf_bessel_zero_Jnu_e($nu, $s, $result)

gsl_sf_bessel_zero_Jnu($nu, $s)

-

gsl_sf_clausen_e($x, $result)

gsl_sf_clausen($x)

-

gsl_sf_hydrogenicR_1_e($Z, $r, $result)

gsl_sf_hydrogenicR_1($Z, $r)

-

gsl_sf_hydrogenicR_e($n, $l, $Z, $r, $result)

gsl_sf_hydrogenicR($n, $l, $Z, $r)

-

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.

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($L, $eta, $result) - This function computes the Coulomb wave function normalization constant C_L($eta) for $L > -1.

gsl_sf_coulomb_CL_arrayi -

gsl_sf_coupling_3j_e($two_ja, $two_jb, $two_jc, $two_ma, $two_mb, $two_mc, $result)

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.

gsl_sf_coupling_6j_e($two_ja, $two_jb, $two_jc, $two_jd, $two_je, $two_jf, $result)

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.

gsl_sf_coupling_RacahW_e

gsl_sf_coupling_RacahW

-

gsl_sf_coupling_9j_e($two_ja, $two_jb, $two_jc, $two_jd, $two_je, $two_jf, $two_jg, $two_jh, $two_ji, $result)

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. 

gsl_sf_dawson_e($x, $result)

gsl_sf_dawson($x)

-These routines compute the value of Dawson's integral for $x.

gsl_sf_debye_1_e($x, $result)

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)).

gsl_sf_debye_2_e($x, $result)

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)).

gsl_sf_debye_3_e($x, $result)

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)).

gsl_sf_debye_4_e($x, $result)

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)).

gsl_sf_debye_5_e($x, $result)

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)).

gsl_sf_debye_6_e($x, $result)

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)).

gsl_sf_dilog_e ($x, $result)

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).

gsl_sf_complex_dilog_xy_e -

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.

gsl_sf_complex_spence_xy_e -

gsl_sf_multiply

gsl_sf_multiply_e($x, $y, $result) - This function multiplies $x and $y storing the product and its associated error in $result.

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.

-

gsl_sf_ellint_Kcomp_e($k, $mode, $result)

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.

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($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.

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_Z

-

gsl_sf_erf_Q_e

gsl_sf_erf_Q

-

gsl_sf_hazard_e

gsl_sf_hazard

-

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

-

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

-

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_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

gsl_sf_taylorcoeff_e

gsl_sf_taylorcoeff

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

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_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

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

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_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

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_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

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

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

gsl_sf_sin_e

gsl_sf_sin

gsl_sf_cos_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

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

gsl_sf_eta_int_e

gsl_sf_eta_int

gsl_sf_eta_e

gsl_sf_eta

This module also contains the following constants used as mode in various of those functions :

• GSL_PREC_DOUBLE - Double-precision, a relative accuracy of approximately 2 * 10^-16.
• GSL_PREC_SINGLE - Single-precision, a relative accuracy of approximately 10^-7.
• GSL_PREC_APPROX - Approximate values, a relative accuracy of approximately 5 * 10^-4.

 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 :

airy

bessel

clausen

hydrogenic

coulumb

coupling

dawson

debye

dilog

factorial

misc

elliptic

error

hypergeometric

laguerre

legendre

gamma

transport

trig

zeta

eta

vars

For more informations on the functions, we refer you to the GSL offcial documentation: 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

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 examples/sf folder of the source code.

AUTHORS

Jonathan Leto <jonathan@leto.net> and Thierry Moisan <thierry.moisan@gmail.com>

COPYRIGHT AND LICENSE

Copyright (C) 2008 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.