praat/external/gsl/gsl_sf_bessel.h

/* 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 3 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_mode.h"
#include "gsl_precision.h"
#include "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__ */