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Diffstat (limited to 'gsl-1.9/specfunc/gsl_sf_bessel.h')
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1 files changed, 548 insertions, 0 deletions
diff --git a/gsl-1.9/specfunc/gsl_sf_bessel.h b/gsl-1.9/specfunc/gsl_sf_bessel.h new file mode 100644 index 0000000..31d42f2 --- /dev/null +++ b/gsl-1.9/specfunc/gsl_sf_bessel.h @@ -0,0 +1,548 @@ +/* specfunc/gsl_sf_bessel.h + * + * Copyright (C) 1996, 1997, 1998, 1999, 2000 Gerard Jungman + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU General Public License as published by + * the Free Software Foundation; either version 2 of the License, or (at + * your option) any later version. + * + * This program is distributed in the hope that it will be useful, but + * WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + * General Public License for more details. + * + * You should have received a copy of the GNU General Public License + * along with this program; if not, write to the Free Software + * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA. + */ + +/* Author: G. Jungman */ + +#ifndef __GSL_SF_BESSEL_H__ +#define __GSL_SF_BESSEL_H__ + +#include <stdlib.h> +#include <gsl/gsl_mode.h> +#include <gsl/gsl_precision.h> +#include <gsl/gsl_sf_result.h> + +#undef __BEGIN_DECLS +#undef __END_DECLS +#ifdef __cplusplus +# define __BEGIN_DECLS extern "C" { +# define __END_DECLS } +#else +# define __BEGIN_DECLS /* empty */ +# define __END_DECLS /* empty */ +#endif + +__BEGIN_DECLS + + +/* Regular Bessel Function J_0(x) + * + * exceptions: none + */ +int gsl_sf_bessel_J0_e(const double x, gsl_sf_result * result); +double gsl_sf_bessel_J0(const double x); + + +/* Regular Bessel Function J_1(x) + * + * exceptions: GSL_EUNDRFLW + */ +int gsl_sf_bessel_J1_e(const double x, gsl_sf_result * result); +double gsl_sf_bessel_J1(const double x); + + +/* Regular Bessel Function J_n(x) + * + * exceptions: GSL_EUNDRFLW + */ +int gsl_sf_bessel_Jn_e(int n, double x, gsl_sf_result * result); +double gsl_sf_bessel_Jn(const int n, const double x); + + +/* Regular Bessel Function J_n(x), nmin <= n <= nmax + * + * exceptions: GSL_EDOM, GSL_EUNDRFLW + */ +int gsl_sf_bessel_Jn_array(int nmin, int nmax, double x, double * result_array); + + +/* Irregular Bessel function Y_0(x) + * + * x > 0.0 + * exceptions: GSL_EDOM, GSL_EUNDRFLW + */ +int gsl_sf_bessel_Y0_e(const double x, gsl_sf_result * result); +double gsl_sf_bessel_Y0(const double x); + + +/* Irregular Bessel function Y_1(x) + * + * x > 0.0 + * exceptions: GSL_EDOM, GSL_EOVRFLW, GSL_EUNDRFLW + */ +int gsl_sf_bessel_Y1_e(const double x, gsl_sf_result * result); +double gsl_sf_bessel_Y1(const double x); + + +/* Irregular Bessel function Y_n(x) + * + * x > 0.0 + * exceptions: GSL_EDOM, GSL_EOVRFLW, GSL_EUNDRFLW + */ +int gsl_sf_bessel_Yn_e(int n,const double x, gsl_sf_result * result); +double gsl_sf_bessel_Yn(const int n,const double x); + + +/* Irregular Bessel function Y_n(x), nmin <= n <= nmax + * + * x > 0.0 + * exceptions: GSL_EDOM, GSL_EOVRFLW, GSL_EUNDRFLW + */ +int gsl_sf_bessel_Yn_array(const int nmin, const int nmax, const double x, double * result_array); + + +/* Regular modified Bessel function I_0(x) + * + * exceptions: GSL_EOVRFLW + */ +int gsl_sf_bessel_I0_e(const double x, gsl_sf_result * result); +double gsl_sf_bessel_I0(const double x); + + +/* Regular modified Bessel function I_1(x) + * + * exceptions: GSL_EOVRFLW, GSL_EUNDRFLW + */ +int gsl_sf_bessel_I1_e(const double x, gsl_sf_result * result); +double gsl_sf_bessel_I1(const double x); + + +/* Regular modified Bessel function I_n(x) + * + * exceptions: GSL_EOVRFLW, GSL_EUNDRFLW + */ +int gsl_sf_bessel_In_e(const int n, const double x, gsl_sf_result * result); +double gsl_sf_bessel_In(const int n, const double x); + + +/* Regular modified Bessel function I_n(x) for n=nmin,...,nmax + * + * nmin >=0, nmax >= nmin + * exceptions: GSL_EDOM, GSL_EOVRFLW, GSL_EUNDRFLW + */ +int gsl_sf_bessel_In_array(const int nmin, const int nmax, const double x, double * result_array); + + +/* Scaled regular modified Bessel function + * exp(-|x|) I_0(x) + * + * exceptions: none + */ +int gsl_sf_bessel_I0_scaled_e(const double x, gsl_sf_result * result); +double gsl_sf_bessel_I0_scaled(const double x); + + +/* Scaled regular modified Bessel function + * exp(-|x|) I_1(x) + * + * exceptions: GSL_EUNDRFLW + */ +int gsl_sf_bessel_I1_scaled_e(const double x, gsl_sf_result * result); +double gsl_sf_bessel_I1_scaled(const double x); + + +/* Scaled regular modified Bessel function + * exp(-|x|) I_n(x) + * + * exceptions: GSL_EUNDRFLW + */ +int gsl_sf_bessel_In_scaled_e(int n, const double x, gsl_sf_result * result); +double gsl_sf_bessel_In_scaled(const int n, const double x); + + +/* Scaled regular modified Bessel function + * exp(-|x|) I_n(x) for n=nmin,...,nmax + * + * nmin >=0, nmax >= nmin + * exceptions: GSL_EUNDRFLW + */ +int gsl_sf_bessel_In_scaled_array(const int nmin, const int nmax, const double x, double * result_array); + + +/* Irregular modified Bessel function K_0(x) + * + * x > 0.0 + * exceptions: GSL_EDOM, GSL_EUNDRFLW + */ +int gsl_sf_bessel_K0_e(const double x, gsl_sf_result * result); +double gsl_sf_bessel_K0(const double x); + + +/* Irregular modified Bessel function K_1(x) + * + * x > 0.0 + * exceptions: GSL_EDOM, GSL_EOVRFLW, GSL_EUNDRFLW + */ +int gsl_sf_bessel_K1_e(const double x, gsl_sf_result * result); +double gsl_sf_bessel_K1(const double x); + + +/* Irregular modified Bessel function K_n(x) + * + * x > 0.0 + * exceptions: GSL_EDOM, GSL_EOVRFLW, GSL_EUNDRFLW + */ +int gsl_sf_bessel_Kn_e(const int n, const double x, gsl_sf_result * result); +double gsl_sf_bessel_Kn(const int n, const double x); + + +/* Irregular modified Bessel function K_n(x) for n=nmin,...,nmax + * + * x > 0.0, nmin >=0, nmax >= nmin + * exceptions: GSL_EDOM, GSL_EOVRFLW, GSL_EUNDRFLW + */ +int gsl_sf_bessel_Kn_array(const int nmin, const int nmax, const double x, double * result_array); + + +/* Scaled irregular modified Bessel function + * exp(x) K_0(x) + * + * x > 0.0 + * exceptions: GSL_EDOM + */ +int gsl_sf_bessel_K0_scaled_e(const double x, gsl_sf_result * result); +double gsl_sf_bessel_K0_scaled(const double x); + + +/* Scaled irregular modified Bessel function + * exp(x) K_1(x) + * + * x > 0.0 + * exceptions: GSL_EDOM, GSL_EUNDRFLW + */ +int gsl_sf_bessel_K1_scaled_e(const double x, gsl_sf_result * result); +double gsl_sf_bessel_K1_scaled(const double x); + + +/* Scaled irregular modified Bessel function + * exp(x) K_n(x) + * + * x > 0.0 + * exceptions: GSL_EDOM, GSL_EUNDRFLW + */ +int gsl_sf_bessel_Kn_scaled_e(int n, const double x, gsl_sf_result * result); +double gsl_sf_bessel_Kn_scaled(const int n, const double x); + + +/* Scaled irregular modified Bessel function exp(x) K_n(x) for n=nmin,...,nmax + * + * x > 0.0, nmin >=0, nmax >= nmin + * exceptions: GSL_EDOM, GSL_EUNDRFLW + */ +int gsl_sf_bessel_Kn_scaled_array(const int nmin, const int nmax, const double x, double * result_array); + + +/* Regular spherical Bessel function j_0(x) = sin(x)/x + * + * exceptions: none + */ +int gsl_sf_bessel_j0_e(const double x, gsl_sf_result * result); +double gsl_sf_bessel_j0(const double x); + + +/* Regular spherical Bessel function j_1(x) = (sin(x)/x - cos(x))/x + * + * exceptions: GSL_EUNDRFLW + */ +int gsl_sf_bessel_j1_e(const double x, gsl_sf_result * result); +double gsl_sf_bessel_j1(const double x); + + +/* Regular spherical Bessel function j_2(x) = ((3/x^2 - 1)sin(x) - 3cos(x)/x)/x + * + * exceptions: GSL_EUNDRFLW + */ +int gsl_sf_bessel_j2_e(const double x, gsl_sf_result * result); +double gsl_sf_bessel_j2(const double x); + + +/* Regular spherical Bessel function j_l(x) + * + * l >= 0, x >= 0.0 + * exceptions: GSL_EDOM, GSL_EUNDRFLW + */ +int gsl_sf_bessel_jl_e(const int l, const double x, gsl_sf_result * result); +double gsl_sf_bessel_jl(const int l, const double x); + + +/* Regular spherical Bessel function j_l(x) for l=0,1,...,lmax + * + * exceptions: GSL_EDOM, GSL_EUNDRFLW + */ +int gsl_sf_bessel_jl_array(const int lmax, const double x, double * result_array); + + +/* Regular spherical Bessel function j_l(x) for l=0,1,...,lmax + * Uses Steed's method. + * + * exceptions: GSL_EDOM, GSL_EUNDRFLW + */ +int gsl_sf_bessel_jl_steed_array(const int lmax, const double x, double * jl_x_array); + + +/* Irregular spherical Bessel function y_0(x) + * + * exceptions: none + */ +int gsl_sf_bessel_y0_e(const double x, gsl_sf_result * result); +double gsl_sf_bessel_y0(const double x); + + +/* Irregular spherical Bessel function y_1(x) + * + * exceptions: GSL_EUNDRFLW + */ +int gsl_sf_bessel_y1_e(const double x, gsl_sf_result * result); +double gsl_sf_bessel_y1(const double x); + + +/* Irregular spherical Bessel function y_2(x) + * + * exceptions: GSL_EUNDRFLW + */ +int gsl_sf_bessel_y2_e(const double x, gsl_sf_result * result); +double gsl_sf_bessel_y2(const double x); + + +/* Irregular spherical Bessel function y_l(x) + * + * exceptions: GSL_EUNDRFLW + */ +int gsl_sf_bessel_yl_e(int l, const double x, gsl_sf_result * result); +double gsl_sf_bessel_yl(const int l, const double x); + + +/* Irregular spherical Bessel function y_l(x) for l=0,1,...,lmax + * + * exceptions: GSL_EUNDRFLW + */ +int gsl_sf_bessel_yl_array(const int lmax, const double x, double * result_array); + + +/* Regular scaled modified spherical Bessel function + * + * Exp[-|x|] i_0(x) + * + * exceptions: none + */ +int gsl_sf_bessel_i0_scaled_e(const double x, gsl_sf_result * result); +double gsl_sf_bessel_i0_scaled(const double x); + + +/* Regular scaled modified spherical Bessel function + * + * Exp[-|x|] i_1(x) + * + * exceptions: GSL_EUNDRFLW + */ +int gsl_sf_bessel_i1_scaled_e(const double x, gsl_sf_result * result); +double gsl_sf_bessel_i1_scaled(const double x); + + +/* Regular scaled modified spherical Bessel function + * + * Exp[-|x|] i_2(x) + * + * exceptions: GSL_EUNDRFLW + */ +int gsl_sf_bessel_i2_scaled_e(const double x, gsl_sf_result * result); +double gsl_sf_bessel_i2_scaled(const double x); + + +/* Regular scaled modified spherical Bessel functions + * + * Exp[-|x|] i_l(x) + * + * i_l(x) = Sqrt[Pi/(2x)] BesselI[l+1/2,x] + * + * l >= 0 + * exceptions: GSL_EDOM, GSL_EUNDRFLW + */ +int gsl_sf_bessel_il_scaled_e(const int l, double x, gsl_sf_result * result); +double gsl_sf_bessel_il_scaled(const int l, const double x); + + +/* Regular scaled modified spherical Bessel functions + * + * Exp[-|x|] i_l(x) + * for l=0,1,...,lmax + * + * exceptions: GSL_EUNDRFLW + */ +int gsl_sf_bessel_il_scaled_array(const int lmax, const double x, double * result_array); + + +/* Irregular scaled modified spherical Bessel function + * Exp[x] k_0(x) + * + * x > 0.0 + * exceptions: GSL_EDOM, GSL_EUNDRFLW + */ +int gsl_sf_bessel_k0_scaled_e(const double x, gsl_sf_result * result); +double gsl_sf_bessel_k0_scaled(const double x); + + +/* Irregular modified spherical Bessel function + * Exp[x] k_1(x) + * + * x > 0.0 + * exceptions: GSL_EDOM, GSL_EUNDRFLW, GSL_EOVRFLW + */ +int gsl_sf_bessel_k1_scaled_e(const double x, gsl_sf_result * result); +double gsl_sf_bessel_k1_scaled(const double x); + + +/* Irregular modified spherical Bessel function + * Exp[x] k_2(x) + * + * x > 0.0 + * exceptions: GSL_EDOM, GSL_EUNDRFLW, GSL_EOVRFLW + */ +int gsl_sf_bessel_k2_scaled_e(const double x, gsl_sf_result * result); +double gsl_sf_bessel_k2_scaled(const double x); + + +/* Irregular modified spherical Bessel function + * Exp[x] k_l[x] + * + * k_l(x) = Sqrt[Pi/(2x)] BesselK[l+1/2,x] + * + * exceptions: GSL_EDOM, GSL_EUNDRFLW + */ +int gsl_sf_bessel_kl_scaled_e(int l, const double x, gsl_sf_result * result); +double gsl_sf_bessel_kl_scaled(const int l, const double x); + + +/* Irregular scaled modified spherical Bessel function + * Exp[x] k_l(x) + * + * for l=0,1,...,lmax + * exceptions: GSL_EDOM, GSL_EUNDRFLW + */ +int gsl_sf_bessel_kl_scaled_array(const int lmax, const double x, double * result_array); + + +/* Regular cylindrical Bessel function J_nu(x) + * + * exceptions: GSL_EDOM, GSL_EUNDRFLW + */ +int gsl_sf_bessel_Jnu_e(const double nu, const double x, gsl_sf_result * result); +double gsl_sf_bessel_Jnu(const double nu, const double x); + + +/* Irregular cylindrical Bessel function Y_nu(x) + * + * exceptions: + */ +int gsl_sf_bessel_Ynu_e(double nu, double x, gsl_sf_result * result); +double gsl_sf_bessel_Ynu(const double nu, const double x); + + +/* Regular cylindrical Bessel function J_nu(x) + * evaluated at a series of x values. The array + * contains the x values. They are assumed to be + * strictly ordered and positive. The array is + * over-written with the values of J_nu(x_i). + * + * exceptions: GSL_EDOM, GSL_EINVAL + */ +int gsl_sf_bessel_sequence_Jnu_e(double nu, gsl_mode_t mode, size_t size, double * v); + + +/* Scaled modified cylindrical Bessel functions + * + * Exp[-|x|] BesselI[nu, x] + * x >= 0, nu >= 0 + * + * exceptions: GSL_EDOM + */ +int gsl_sf_bessel_Inu_scaled_e(double nu, double x, gsl_sf_result * result); +double gsl_sf_bessel_Inu_scaled(double nu, double x); + + +/* Modified cylindrical Bessel functions + * + * BesselI[nu, x] + * x >= 0, nu >= 0 + * + * exceptions: GSL_EDOM, GSL_EOVRFLW + */ +int gsl_sf_bessel_Inu_e(double nu, double x, gsl_sf_result * result); +double gsl_sf_bessel_Inu(double nu, double x); + + +/* Scaled modified cylindrical Bessel functions + * + * Exp[+|x|] BesselK[nu, x] + * x > 0, nu >= 0 + * + * exceptions: GSL_EDOM + */ +int gsl_sf_bessel_Knu_scaled_e(const double nu, const double x, gsl_sf_result * result); +double gsl_sf_bessel_Knu_scaled(const double nu, const double x); + + +/* Modified cylindrical Bessel functions + * + * BesselK[nu, x] + * x > 0, nu >= 0 + * + * exceptions: GSL_EDOM, GSL_EUNDRFLW + */ +int gsl_sf_bessel_Knu_e(const double nu, const double x, gsl_sf_result * result); +double gsl_sf_bessel_Knu(const double nu, const double x); + + +/* Logarithm of modified cylindrical Bessel functions. + * + * Log[BesselK[nu, x]] + * x > 0, nu >= 0 + * + * exceptions: GSL_EDOM + */ +int gsl_sf_bessel_lnKnu_e(const double nu, const double x, gsl_sf_result * result); +double gsl_sf_bessel_lnKnu(const double nu, const double x); + + +/* s'th positive zero of the Bessel function J_0(x). + * + * exceptions: + */ +int gsl_sf_bessel_zero_J0_e(unsigned int s, gsl_sf_result * result); +double gsl_sf_bessel_zero_J0(unsigned int s); + + +/* s'th positive zero of the Bessel function J_1(x). + * + * exceptions: + */ +int gsl_sf_bessel_zero_J1_e(unsigned int s, gsl_sf_result * result); +double gsl_sf_bessel_zero_J1(unsigned int s); + + +/* s'th positive zero of the Bessel function J_nu(x). + * + * exceptions: + */ +int gsl_sf_bessel_zero_Jnu_e(double nu, unsigned int s, gsl_sf_result * result); +double gsl_sf_bessel_zero_Jnu(double nu, unsigned int s); + + +__END_DECLS + +#endif /* __GSL_SF_BESSEL_H__ */ |