Math::GSL::SF - Special Functions
use Math::GSL::SF qw /:all/;
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_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 $n, Y_n(x), for x>0.
gsl_sf_bessel_I0_e($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 $n, I_n(x).
gsl_sf_bessel_I0_scaled_e($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 $n, \exp(-|x|) I_n(x)
gsl_sf_bessel_K0_e($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 $n, K_n(x), for x > 0.
gsl_sf_bessel_K0_scaled_e($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_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 = $two_ma/2, etc.
gsl_sf_coupling_9j_e($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 $result_im gsl_result structs.gsl_sf_complex_spence_xy_e -gsl_sf_multiplygsl_sf_multiply_e($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_F_e($phi, $k, $mode, $result)gsl_sf_ellint_F($phi, $k, $mode)-These routines compute the incomplete elliptic integral F($phi,$k) to the accuracy specified by the mode variable mode. Note that Abramowitz & Stegun define this function in terms of the parameter m = k^2.
gsl_sf_ellint_E_e($phi, $k, $mode, $result)gsl_sf_ellint_E($phi, $k, $mode)-These routines compute the incomplete elliptic integral E($phi,$k) to the accuracy specified by the mode variable mode. Note that Abramowitz & Stegun define this function in terms of the parameter m = k^2.
gsl_sf_ellint_P_e($phi, $k, $n, $mode, $result)gsl_sf_ellint_P($phi, $k, $n, $mode)-These routines compute the incomplete elliptic integral \Pi(\phi,k,n) to the accuracy specified by the mode variable mode. Note that Abramowitz & Stegun define this function in terms of the parameters m = k^2 and \sin^2(\alpha) = k^2, with the change of sign n \to -n.
gsl_sf_ellint_D_e($phi, $k, $n, $mode, $result)gsl_sf_ellint_D($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 $n is not used and will be removed in a future release.
gsl_sf_ellint_RC_e($x, $y, $mode, $result)gsl_sf_ellint_RC($x, $y, $mode)- These routines compute the incomplete elliptic integral RC($x,$y) to the accuracy specified by the mode variable $mode.
gsl_sf_ellint_RD_e($x, $y, $z, $mode, $result)gsl_sf_ellint_RD($x, $y, $z, $mode)- These routines compute the incomplete elliptic integral RD($x,$y,$z) to the accuracy specified by the mode variable $mode.
gsl_sf_ellint_RF_e($x, $y, $z, $mode, $result)gsl_sf_ellint_RF($x, $y, $z, $mode)- These routines compute the incomplete elliptic integral RF($x,$y,$z) to the accuracy specified by the mode variable $mode.
gsl_sf_ellint_RJ_e($x, $y, $z, $p, $mode, $result)gsl_sf_ellint_RJ($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 $mode.
gsl_sf_elljac_e($u, $m) - This function computes the Jacobian elliptic functions sn(u|m), cn(u|m), dn(u|m) by descending Landen transformations. The function returns 0 if the operation succeded, 1 otherwise and then returns the result of sn, cn and dn in this order.gsl_sf_erfc_e($x, $result)gsl_sf_erfc($x)-These routines compute the complementary error function erfc(x) = 1 - erf(x) = (2/\sqrt(\pi)) \int_x^\infty \exp(-t^2).
gsl_sf_log_erfc_e($x, $result)gsl_sf_log_erfc($x)-These routines compute the logarithm of the complementary error function \log(\erfc(x)).
gsl_sf_erf_e($x, $result)gsl_sf_erf($x)-These routines compute the error function erf(x), where erf(x) = (2/\sqrt(\pi)) \int_0^x dt \exp(-t^2).
gsl_sf_erf_Z_e($x, $result)gsl_sf_erf_Z($x)-These routines compute the Gaussian probability density function Z(x) = (1/\sqrt{2\pi}) \exp(-x^2/2).
gsl_sf_erf_Q_e($x, $result)gsl_sf_erf_Q($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.
gsl_sf_hazard_e($x, $result)gsl_sf_hazard($x)- These routines compute the hazard function for the normal distribution.
gsl_sf_exp_e($x, $result)gsl_sf_exp($x)- These routines provide an exponential function \exp(x) using GSL semantics and error checking.
gsl_sf_expm1_e($x, $result)gsl_sf_expm1($x)-These routines compute the quantity \exp(x)-1 using an algorithm that is accurate for small x.
gsl_sf_exprel_e($x, $result)gsl_sf_exprel($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.
gsl_sf_exprel_2_e($x, $result)gsl_sf_exprel_2($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.
gsl_sf_exprel_n_e($x, $result)gsl_sf_exprel_n($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)
gsl_sf_exp_err_e($x, $dx, $result) - This function exponentiates $x with an associated absolute error $dx.gsl_sf_exp_err_e10_e -gsl_sf_exp_mult_err_e($x, $dx, $y, $dy, $result) -gsl_sf_exp_mult_err_e10_e -gsl_sf_expint_E1_e($x, $result)gsl_sf_expint_E1($x)-These routines compute the exponential integral E_1(x), E_1(x) := \Re \int_1^\infty dt \exp(-xt)/t.
gsl_sf_expint_E2_e($x, $result)gsl_sf_expint_E2($x)-These routines compute the second-order exponential integral E_2(x), E_2(x) := \Re \int_1^\infty dt \exp(-xt)/t^2.
gsl_sf_expint_En_e($n, $x, $result)gsl_sf_expint_En($n, $x)-These routines compute the exponential integral E_n(x) of order n, E_n(x) := \Re \int_1^\infty dt \exp(-xt)/t^n.
gsl_sf_expint_Ei_e($x, $result)gsl_sf_expint_Ei($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.
gsl_sf_Shi_e($x, $result)gsl_sf_Shi($x)-These routines compute the integral Shi(x) = \int_0^x dt \sinh(t)/t.
gsl_sf_Chi_e($x, $result)gsl_sf_Chi($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 $M_EULER from the Math::GSL::Const module).
gsl_sf_expint_3_e($x, $result)gsl_sf_expint_3($x)-These routines compute the third-order exponential integral Ei_3(x) = \int_0^xdt \exp(-t^3) for x >= 0.
gsl_sf_Si_e($x, $result)gsl_sf_Si($x)-These routines compute the Sine integral Si(x) = \int_0^x dt \sin(t)/t.
gsl_sf_Ci_e($x, $result)gsl_sf_Ci($x)-These routines compute the Cosine integral Ci(x) = -\int_x^\infty dt \cos(t)/t for x > 0.
gsl_sf_fermi_dirac_m1_e($x, $result)gsl_sf_fermi_dirac_m1($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).
gsl_sf_fermi_dirac_0_e($x, $result)gsl_sf_fermi_dirac_0($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).
gsl_sf_fermi_dirac_1_e($x, $result)gsl_sf_fermi_dirac_1($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)).
gsl_sf_fermi_dirac_2_e($x, $result)gsl_sf_fermi_dirac_2($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)).
gsl_sf_fermi_dirac_int_e($j, $x, $result)gsl_sf_fermi_dirac_int($j, $x)-These routines compute the complete Fermi-Dirac integral with an integer index of j, F_j(x) = (1/\Gamma(j+1)) \int_0^\infty dt (t^j /(\exp(t-x)+1)).
gsl_sf_fermi_dirac_mhalf_e($x, $result)gsl_sf_fermi_dirac_mhalf($x)-These routines compute the complete Fermi-Dirac integral F_{-1/2}(x).
gsl_sf_fermi_dirac_half_e($x, $result)gsl_sf_fermi_dirac_half($x)-These routines compute the complete Fermi-Dirac integral F_{1/2}(x).
gsl_sf_fermi_dirac_3half_e($x, $result)gsl_sf_fermi_dirac_3half($x)-These routines compute the complete Fermi-Dirac integral F_{3/2}(x).
gsl_sf_fermi_dirac_inc_0_e($x, $b, $result)gsl_sf_fermi_dirac_inc_0($x, $b, $result)-These routines compute the incomplete Fermi-Dirac integral with an index of zero, F_0(x,b) = \ln(1 + e^{b-x}) - (b-x).
gsl_sf_legendre_Pl_e($l, $x, $result)gsl_sf_legendre_Pl($l, $x)-These functions evaluate the Legendre polynomial P_l(x) for a specific value of l, x subject to l >= 0, |x| <= 1
gsl_sf_legendre_P1_e($x, $result)gsl_sf_legendre_P2_e($x, $result)gsl_sf_legendre_P3_e($x, $result)gsl_sf_legendre_P1($x)gsl_sf_legendre_P2($x)gsl_sf_legendre_P3($x)-These functions evaluate the Legendre polynomials P_l(x) using explicit representations for l=1, 2, 3.
gsl_sf_legendre_Q0_e($x, $result)gsl_sf_legendre_Q0($x)-These routines compute the Legendre function Q_0(x) for x > -1, x != 1.
gsl_sf_legendre_Q1_e($x, $result)gsl_sf_legendre_Q1($x)-These routines compute the Legendre function Q_1(x) for x > -1, x != 1.
gsl_sf_legendre_Ql_e($l, $x, $result)gsl_sf_legendre_Ql($l, $x)-These routines compute the Legendre function Q_l(x) for x > -1, x != 1 and l >= 0.
gsl_sf_legendre_Plm_e($l, $m, $x, $result)gsl_sf_legendre_Plm($l, $m, $x)-These routines compute the associated Legendre polynomial P_l^m(x) for m >= 0, l >= m, |x| <= 1.
gsl_sf_legendre_sphPlm_e($l, $m, $x, $result)gsl_sf_legendre_sphPlm($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).
gsl_sf_lngamma_e($x, $result)gsl_sf_lngamma($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.
gsl_sf_gegenpoly_1_egsl_sf_gegenpoly_2_e gsl_sf_gegenpoly_3_egsl_sf_gegenpoly_1gsl_sf_gegenpoly_2 gsl_sf_gegenpoly_3-
gsl_sf_laguerre_1_e gsl_sf_laguerre_2_egsl_sf_laguerre_3_egsl_sf_laguerre_1 gsl_sf_laguerre_2gsl_sf_laguerre_3-
gsl_sf_angle_restrict_symm_err_egsl_sf_angle_restrict_pos_err_e gsl_sf_atanint_egsl_sf_atanint-These routines compute the Arctangent integral, which is defined as AtanInt(x) = \int_0^x dt \arctan(t)/t.
gsl_sf_zeta_int_e gsl_sf_zeta_intgsl_sf_zeta_e gsl_sf_zeta gsl_sf_zetam1_egsl_sf_zetam1gsl_sf_zetam1_int_e gsl_sf_zetam1_intgsl_sf_hzeta_egsl_sf_hzeta gsl_sf_eta_int_egsl_sf_eta_intgsl_sf_eta_egsl_sf_eta This module also contains the following constants used as mode in various of those functions :
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 :
airybesselclausenhydrogeniccoulumbcouplingdawsondebyedilogfactorialmiscellipticerrorhypergeometriclaguerrelegendregammatransporttrigzetaetavarsFor 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
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.
Jonathan Leto <jonathan@leto.net> and Thierry Moisan <thierry.moisan@gmail.com>
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.
