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/* specfunc/gsl_sf_bessel.h
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*
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* Copyright (C) 1996, 1997, 1998, 1999, 2000 Gerard Jungman
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*
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* This program is free software; you can redistribute it and/or modify
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* it under the terms of the GNU General Public License as published by
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* the Free Software Foundation; either version 3 of the License, or (at
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* your option) any later version.
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*
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* This program is distributed in the hope that it will be useful, but
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* WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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* General Public License for more details.
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*
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* You should have received a copy of the GNU General Public License
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* along with this program; if not, write to the Free Software
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* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
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*/
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/* Author: G. Jungman */
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#ifndef __GSL_SF_BESSEL_H__
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#define __GSL_SF_BESSEL_H__
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#include <stdlib.h>
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#include <gsl/gsl_mode.h>
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#include <gsl/gsl_precision.h>
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#include <gsl/gsl_sf_result.h>
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#undef __BEGIN_DECLS
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#undef __END_DECLS
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#ifdef __cplusplus
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# define __BEGIN_DECLS extern "C" {
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# define __END_DECLS }
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#else
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# define __BEGIN_DECLS /* empty */
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# define __END_DECLS /* empty */
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#endif
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__BEGIN_DECLS
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/* Regular Bessel Function J_0(x)
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*
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* exceptions: none
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*/
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int gsl_sf_bessel_J0_e(const double x, gsl_sf_result * result);
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double gsl_sf_bessel_J0(const double x);
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/* Regular Bessel Function J_1(x)
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*
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* exceptions: GSL_EUNDRFLW
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*/
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int gsl_sf_bessel_J1_e(const double x, gsl_sf_result * result);
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double gsl_sf_bessel_J1(const double x);
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/* Regular Bessel Function J_n(x)
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*
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* exceptions: GSL_EUNDRFLW
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*/
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int gsl_sf_bessel_Jn_e(int n, double x, gsl_sf_result * result);
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double gsl_sf_bessel_Jn(const int n, const double x);
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/* Regular Bessel Function J_n(x), nmin <= n <= nmax
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*
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* exceptions: GSL_EDOM, GSL_EUNDRFLW
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*/
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int gsl_sf_bessel_Jn_array(int nmin, int nmax, double x, double * result_array);
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/* Irregular Bessel function Y_0(x)
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*
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* x > 0.0
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* exceptions: GSL_EDOM, GSL_EUNDRFLW
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*/
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int gsl_sf_bessel_Y0_e(const double x, gsl_sf_result * result);
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double gsl_sf_bessel_Y0(const double x);
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/* Irregular Bessel function Y_1(x)
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*
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* x > 0.0
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* exceptions: GSL_EDOM, GSL_EOVRFLW, GSL_EUNDRFLW
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*/
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int gsl_sf_bessel_Y1_e(const double x, gsl_sf_result * result);
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double gsl_sf_bessel_Y1(const double x);
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/* Irregular Bessel function Y_n(x)
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*
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* x > 0.0
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* exceptions: GSL_EDOM, GSL_EOVRFLW, GSL_EUNDRFLW
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*/
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int gsl_sf_bessel_Yn_e(int n,const double x, gsl_sf_result * result);
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double gsl_sf_bessel_Yn(const int n,const double x);
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/* Irregular Bessel function Y_n(x), nmin <= n <= nmax
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*
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* x > 0.0
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* exceptions: GSL_EDOM, GSL_EOVRFLW, GSL_EUNDRFLW
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*/
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int gsl_sf_bessel_Yn_array(const int nmin, const int nmax, const double x, double * result_array);
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/* Regular modified Bessel function I_0(x)
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*
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* exceptions: GSL_EOVRFLW
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*/
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int gsl_sf_bessel_I0_e(const double x, gsl_sf_result * result);
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double gsl_sf_bessel_I0(const double x);
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/* Regular modified Bessel function I_1(x)
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*
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* exceptions: GSL_EOVRFLW, GSL_EUNDRFLW
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*/
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int gsl_sf_bessel_I1_e(const double x, gsl_sf_result * result);
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double gsl_sf_bessel_I1(const double x);
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/* Regular modified Bessel function I_n(x)
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*
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* exceptions: GSL_EOVRFLW, GSL_EUNDRFLW
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*/
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int gsl_sf_bessel_In_e(const int n, const double x, gsl_sf_result * result);
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double gsl_sf_bessel_In(const int n, const double x);
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/* Regular modified Bessel function I_n(x) for n=nmin,...,nmax
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*
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* nmin >=0, nmax >= nmin
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* exceptions: GSL_EDOM, GSL_EOVRFLW, GSL_EUNDRFLW
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*/
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int gsl_sf_bessel_In_array(const int nmin, const int nmax, const double x, double * result_array);
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/* Scaled regular modified Bessel function
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* exp(-|x|) I_0(x)
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*
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* exceptions: none
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*/
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int gsl_sf_bessel_I0_scaled_e(const double x, gsl_sf_result * result);
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double gsl_sf_bessel_I0_scaled(const double x);
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/* Scaled regular modified Bessel function
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* exp(-|x|) I_1(x)
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*
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* exceptions: GSL_EUNDRFLW
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*/
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int gsl_sf_bessel_I1_scaled_e(const double x, gsl_sf_result * result);
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double gsl_sf_bessel_I1_scaled(const double x);
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/* Scaled regular modified Bessel function
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* exp(-|x|) I_n(x)
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*
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* exceptions: GSL_EUNDRFLW
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*/
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int gsl_sf_bessel_In_scaled_e(int n, const double x, gsl_sf_result * result);
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double gsl_sf_bessel_In_scaled(const int n, const double x);
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/* Scaled regular modified Bessel function
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* exp(-|x|) I_n(x) for n=nmin,...,nmax
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*
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* nmin >=0, nmax >= nmin
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* exceptions: GSL_EUNDRFLW
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*/
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int gsl_sf_bessel_In_scaled_array(const int nmin, const int nmax, const double x, double * result_array);
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/* Irregular modified Bessel function K_0(x)
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*
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* x > 0.0
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* exceptions: GSL_EDOM, GSL_EUNDRFLW
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*/
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int gsl_sf_bessel_K0_e(const double x, gsl_sf_result * result);
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double gsl_sf_bessel_K0(const double x);
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/* Irregular modified Bessel function K_1(x)
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*
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* x > 0.0
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* exceptions: GSL_EDOM, GSL_EOVRFLW, GSL_EUNDRFLW
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*/
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int gsl_sf_bessel_K1_e(const double x, gsl_sf_result * result);
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double gsl_sf_bessel_K1(const double x);
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/* Irregular modified Bessel function K_n(x)
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*
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* x > 0.0
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* exceptions: GSL_EDOM, GSL_EOVRFLW, GSL_EUNDRFLW
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*/
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int gsl_sf_bessel_Kn_e(const int n, const double x, gsl_sf_result * result);
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double gsl_sf_bessel_Kn(const int n, const double x);
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/* Irregular modified Bessel function K_n(x) for n=nmin,...,nmax
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*
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* x > 0.0, nmin >=0, nmax >= nmin
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* exceptions: GSL_EDOM, GSL_EOVRFLW, GSL_EUNDRFLW
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*/
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int gsl_sf_bessel_Kn_array(const int nmin, const int nmax, const double x, double * result_array);
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/* Scaled irregular modified Bessel function
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* exp(x) K_0(x)
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*
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* x > 0.0
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* exceptions: GSL_EDOM
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*/
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int gsl_sf_bessel_K0_scaled_e(const double x, gsl_sf_result * result);
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double gsl_sf_bessel_K0_scaled(const double x);
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/* Scaled irregular modified Bessel function
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* exp(x) K_1(x)
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*
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* x > 0.0
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* exceptions: GSL_EDOM, GSL_EUNDRFLW
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*/
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int gsl_sf_bessel_K1_scaled_e(const double x, gsl_sf_result * result);
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double gsl_sf_bessel_K1_scaled(const double x);
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/* Scaled irregular modified Bessel function
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* exp(x) K_n(x)
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*
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* x > 0.0
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* exceptions: GSL_EDOM, GSL_EUNDRFLW
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*/
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int gsl_sf_bessel_Kn_scaled_e(int n, const double x, gsl_sf_result * result);
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double gsl_sf_bessel_Kn_scaled(const int n, const double x);
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/* Scaled irregular modified Bessel function exp(x) K_n(x) for n=nmin,...,nmax
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*
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* x > 0.0, nmin >=0, nmax >= nmin
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* exceptions: GSL_EDOM, GSL_EUNDRFLW
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*/
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int gsl_sf_bessel_Kn_scaled_array(const int nmin, const int nmax, const double x, double * result_array);
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/* Regular spherical Bessel function j_0(x) = sin(x)/x
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*
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* exceptions: none
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*/
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int gsl_sf_bessel_j0_e(const double x, gsl_sf_result * result);
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double gsl_sf_bessel_j0(const double x);
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/* Regular spherical Bessel function j_1(x) = (sin(x)/x - cos(x))/x
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*
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* exceptions: GSL_EUNDRFLW
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*/
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int gsl_sf_bessel_j1_e(const double x, gsl_sf_result * result);
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double gsl_sf_bessel_j1(const double x);
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/* Regular spherical Bessel function j_2(x) = ((3/x^2 - 1)sin(x) - 3cos(x)/x)/x
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*
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* exceptions: GSL_EUNDRFLW
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*/
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int gsl_sf_bessel_j2_e(const double x, gsl_sf_result * result);
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double gsl_sf_bessel_j2(const double x);
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/* Regular spherical Bessel function j_l(x)
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*
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* l >= 0, x >= 0.0
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* exceptions: GSL_EDOM, GSL_EUNDRFLW
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*/
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int gsl_sf_bessel_jl_e(const int l, const double x, gsl_sf_result * result);
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double gsl_sf_bessel_jl(const int l, const double x);
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/* Regular spherical Bessel function j_l(x) for l=0,1,...,lmax
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*
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* exceptions: GSL_EDOM, GSL_EUNDRFLW
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*/
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int gsl_sf_bessel_jl_array(const int lmax, const double x, double * result_array);
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/* Regular spherical Bessel function j_l(x) for l=0,1,...,lmax
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* Uses Steed's method.
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*
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* exceptions: GSL_EDOM, GSL_EUNDRFLW
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*/
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int gsl_sf_bessel_jl_steed_array(const int lmax, const double x, double * jl_x_array);
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/* Irregular spherical Bessel function y_0(x)
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*
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* exceptions: none
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*/
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int gsl_sf_bessel_y0_e(const double x, gsl_sf_result * result);
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double gsl_sf_bessel_y0(const double x);
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/* Irregular spherical Bessel function y_1(x)
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*
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* exceptions: GSL_EUNDRFLW
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*/
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int gsl_sf_bessel_y1_e(const double x, gsl_sf_result * result);
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double gsl_sf_bessel_y1(const double x);
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/* Irregular spherical Bessel function y_2(x)
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*
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* exceptions: GSL_EUNDRFLW
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*/
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int gsl_sf_bessel_y2_e(const double x, gsl_sf_result * result);
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double gsl_sf_bessel_y2(const double x);
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/* Irregular spherical Bessel function y_l(x)
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*
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* exceptions: GSL_EUNDRFLW
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*/
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int gsl_sf_bessel_yl_e(int l, const double x, gsl_sf_result * result);
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double gsl_sf_bessel_yl(const int l, const double x);
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/* Irregular spherical Bessel function y_l(x) for l=0,1,...,lmax
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*
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* exceptions: GSL_EUNDRFLW
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*/
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int gsl_sf_bessel_yl_array(const int lmax, const double x, double * result_array);
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/* Regular scaled modified spherical Bessel function
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*
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* Exp[-|x|] i_0(x)
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*
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* exceptions: none
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*/
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int gsl_sf_bessel_i0_scaled_e(const double x, gsl_sf_result * result);
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double gsl_sf_bessel_i0_scaled(const double x);
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/* Regular scaled modified spherical Bessel function
|
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*
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* Exp[-|x|] i_1(x)
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*
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* exceptions: GSL_EUNDRFLW
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*/
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int gsl_sf_bessel_i1_scaled_e(const double x, gsl_sf_result * result);
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double gsl_sf_bessel_i1_scaled(const double x);
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/* Regular scaled modified spherical Bessel function
|
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*
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* Exp[-|x|] i_2(x)
|
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*
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* exceptions: GSL_EUNDRFLW
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*/
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int gsl_sf_bessel_i2_scaled_e(const double x, gsl_sf_result * result);
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double gsl_sf_bessel_i2_scaled(const double x);
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/* Regular scaled modified spherical Bessel functions
|
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*
|
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* Exp[-|x|] i_l(x)
|
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*
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* i_l(x) = Sqrt[Pi/(2x)] BesselI[l+1/2,x]
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*
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* l >= 0
|
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* exceptions: GSL_EDOM, GSL_EUNDRFLW
|
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*/
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int gsl_sf_bessel_il_scaled_e(const int l, double x, gsl_sf_result * result);
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double gsl_sf_bessel_il_scaled(const int l, const double x);
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|
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/* Regular scaled modified spherical Bessel functions
|
|
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*
|
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* Exp[-|x|] i_l(x)
|
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* for l=0,1,...,lmax
|
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*
|
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* exceptions: GSL_EUNDRFLW
|
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*/
|
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int gsl_sf_bessel_il_scaled_array(const int lmax, const double x, double * result_array);
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|
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/* Irregular scaled modified spherical Bessel function
|
|
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* Exp[x] k_0(x)
|
|
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*
|
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* x > 0.0
|
|
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* exceptions: GSL_EDOM, GSL_EUNDRFLW
|
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*/
|
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int gsl_sf_bessel_k0_scaled_e(const double x, gsl_sf_result * result);
|
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double gsl_sf_bessel_k0_scaled(const double x);
|
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|
|
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/* Irregular modified spherical Bessel function
|
|
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* Exp[x] k_1(x)
|
|
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*
|
|
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* x > 0.0
|
|
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* exceptions: GSL_EDOM, GSL_EUNDRFLW, GSL_EOVRFLW
|
|
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*/
|
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int gsl_sf_bessel_k1_scaled_e(const double x, gsl_sf_result * result);
|
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double gsl_sf_bessel_k1_scaled(const double x);
|
|
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|
|
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|
|
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/* Irregular modified spherical Bessel function
|
|
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* Exp[x] k_2(x)
|
|
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*
|
|
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* x > 0.0
|
|
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* exceptions: GSL_EDOM, GSL_EUNDRFLW, GSL_EOVRFLW
|
|
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*/
|
|
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int gsl_sf_bessel_k2_scaled_e(const double x, gsl_sf_result * result);
|
|
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double gsl_sf_bessel_k2_scaled(const double x);
|
|
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|
|
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|
|
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/* Irregular modified spherical Bessel function
|
|
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* Exp[x] k_l[x]
|
|
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*
|
|
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* k_l(x) = Sqrt[Pi/(2x)] BesselK[l+1/2,x]
|
|
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*
|
|
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* exceptions: GSL_EDOM, GSL_EUNDRFLW
|
|
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*/
|
|
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int gsl_sf_bessel_kl_scaled_e(int l, const double x, gsl_sf_result * result);
|
|
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double gsl_sf_bessel_kl_scaled(const int l, const double x);
|
|
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|
|
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|
|
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/* Irregular scaled modified spherical Bessel function
|
|
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* Exp[x] k_l(x)
|
|
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*
|
|
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* for l=0,1,...,lmax
|
|
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* exceptions: GSL_EDOM, GSL_EUNDRFLW
|
|
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*/
|
|
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int gsl_sf_bessel_kl_scaled_array(const int lmax, const double x, double * result_array);
|
|
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|
|
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|
|
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/* Regular cylindrical Bessel function J_nu(x)
|
|
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*
|
|
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* exceptions: GSL_EDOM, GSL_EUNDRFLW
|
|
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*/
|
|
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int gsl_sf_bessel_Jnu_e(const double nu, const double x, gsl_sf_result * result);
|
|
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double gsl_sf_bessel_Jnu(const double nu, const double x);
|
|
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|
|
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|
|
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/* Irregular cylindrical Bessel function Y_nu(x)
|
|
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*
|
|
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* exceptions:
|
|
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*/
|
|
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int gsl_sf_bessel_Ynu_e(double nu, double x, gsl_sf_result * result);
|
|
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double gsl_sf_bessel_Ynu(const double nu, const double x);
|
|
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|
|
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|
|
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/* Regular cylindrical Bessel function J_nu(x)
|
|
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* evaluated at a series of x values. The array
|
|
Packit |
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* contains the x values. They are assumed to be
|
|
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* strictly ordered and positive. The array is
|
|
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* over-written with the values of J_nu(x_i).
|
|
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*
|
|
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* exceptions: GSL_EDOM, GSL_EINVAL
|
|
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*/
|
|
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int gsl_sf_bessel_sequence_Jnu_e(double nu, gsl_mode_t mode, size_t size, double * v);
|
|
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|
|
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|
|
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/* Scaled modified cylindrical Bessel functions
|
|
Packit |
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*
|
|
Packit |
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* Exp[-|x|] BesselI[nu, x]
|
|
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* x >= 0, nu >= 0
|
|
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*
|
|
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* exceptions: GSL_EDOM
|
|
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*/
|
|
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int gsl_sf_bessel_Inu_scaled_e(double nu, double x, gsl_sf_result * result);
|
|
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double gsl_sf_bessel_Inu_scaled(double nu, double x);
|
|
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|
|
Packit |
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|
|
Packit |
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/* Modified cylindrical Bessel functions
|
|
Packit |
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*
|
|
Packit |
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* BesselI[nu, x]
|
|
Packit |
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* x >= 0, nu >= 0
|
|
Packit |
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*
|
|
Packit |
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* exceptions: GSL_EDOM, GSL_EOVRFLW
|
|
Packit |
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*/
|
|
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int gsl_sf_bessel_Inu_e(double nu, double x, gsl_sf_result * result);
|
|
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double gsl_sf_bessel_Inu(double nu, double x);
|
|
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|
|
Packit |
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|
|
Packit |
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/* Scaled modified cylindrical Bessel functions
|
|
Packit |
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*
|
|
Packit |
67cb25 |
* Exp[+|x|] BesselK[nu, x]
|
|
Packit |
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* x > 0, nu >= 0
|
|
Packit |
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*
|
|
Packit |
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* exceptions: GSL_EDOM
|
|
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*/
|
|
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int gsl_sf_bessel_Knu_scaled_e(const double nu, const double x, gsl_sf_result * result);
|
|
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double gsl_sf_bessel_Knu_scaled(const double nu, const double x);
|
|
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|
|
Packit |
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int gsl_sf_bessel_Knu_scaled_e10_e(const double nu, const double x, gsl_sf_result_e10 * result);
|
|
Packit |
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|
|
Packit |
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/* Modified cylindrical Bessel functions
|
|
Packit |
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*
|
|
Packit |
67cb25 |
* BesselK[nu, x]
|
|
Packit |
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* x > 0, nu >= 0
|
|
Packit |
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*
|
|
Packit |
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* exceptions: GSL_EDOM, GSL_EUNDRFLW
|
|
Packit |
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*/
|
|
Packit |
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int gsl_sf_bessel_Knu_e(const double nu, const double x, gsl_sf_result * result);
|
|
Packit |
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double gsl_sf_bessel_Knu(const double nu, const double x);
|
|
Packit |
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|
|
Packit |
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|
|
Packit |
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/* Logarithm of modified cylindrical Bessel functions.
|
|
Packit |
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*
|
|
Packit |
67cb25 |
* Log[BesselK[nu, x]]
|
|
Packit |
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* x > 0, nu >= 0
|
|
Packit |
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*
|
|
Packit |
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* exceptions: GSL_EDOM
|
|
Packit |
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*/
|
|
Packit |
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int gsl_sf_bessel_lnKnu_e(const double nu, const double x, gsl_sf_result * result);
|
|
Packit |
67cb25 |
double gsl_sf_bessel_lnKnu(const double nu, const double x);
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
|
|
Packit |
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/* s'th positive zero of the Bessel function J_0(x).
|
|
Packit |
67cb25 |
*
|
|
Packit |
67cb25 |
* exceptions:
|
|
Packit |
67cb25 |
*/
|
|
Packit |
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int gsl_sf_bessel_zero_J0_e(unsigned int s, gsl_sf_result * result);
|
|
Packit |
67cb25 |
double gsl_sf_bessel_zero_J0(unsigned int s);
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
/* s'th positive zero of the Bessel function J_1(x).
|
|
Packit |
67cb25 |
*
|
|
Packit |
67cb25 |
* exceptions:
|
|
Packit |
67cb25 |
*/
|
|
Packit |
67cb25 |
int gsl_sf_bessel_zero_J1_e(unsigned int s, gsl_sf_result * result);
|
|
Packit |
67cb25 |
double gsl_sf_bessel_zero_J1(unsigned int s);
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
/* s'th positive zero of the Bessel function J_nu(x).
|
|
Packit |
67cb25 |
*
|
|
Packit |
67cb25 |
* exceptions:
|
|
Packit |
67cb25 |
*/
|
|
Packit |
67cb25 |
int gsl_sf_bessel_zero_Jnu_e(double nu, unsigned int s, gsl_sf_result * result);
|
|
Packit |
67cb25 |
double gsl_sf_bessel_zero_Jnu(double nu, unsigned int s);
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
|
|
Packit |
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__END_DECLS
|
|
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|
|
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#endif /* __GSL_SF_BESSEL_H__ */
|