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/* specfunc/bessel_amp_phase.c
*
* 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 */
#include <config.h>
#include <gsl/gsl_math.h>
#include <gsl/gsl_errno.h>
#include <gsl/gsl_sf_bessel.h>
#include "bessel_amp_phase.h"
/* chebyshev expansions for amplitude and phase
functions used in bessel evaluations
These are the same for J0,Y0 and for J1,Y1, so
they sit outside those functions.
*/
static double bm0_data[21] = {
0.09284961637381644,
-0.00142987707403484,
0.00002830579271257,
-0.00000143300611424,
0.00000012028628046,
-0.00000001397113013,
0.00000000204076188,
-0.00000000035399669,
0.00000000007024759,
-0.00000000001554107,
0.00000000000376226,
-0.00000000000098282,
0.00000000000027408,
-0.00000000000008091,
0.00000000000002511,
-0.00000000000000814,
0.00000000000000275,
-0.00000000000000096,
0.00000000000000034,
-0.00000000000000012,
0.00000000000000004
};
const cheb_series _gsl_sf_bessel_amp_phase_bm0_cs = {
bm0_data,
20,
-1, 1,
10
};
static double bth0_data[24] = {
-0.24639163774300119,
0.001737098307508963,
-0.000062183633402968,
0.000004368050165742,
-0.000000456093019869,
0.000000062197400101,
-0.000000010300442889,
0.000000001979526776,
-0.000000000428198396,
0.000000000102035840,
-0.000000000026363898,
0.000000000007297935,
-0.000000000002144188,
0.000000000000663693,
-0.000000000000215126,
0.000000000000072659,
-0.000000000000025465,
0.000000000000009229,
-0.000000000000003448,
0.000000000000001325,
-0.000000000000000522,
0.000000000000000210,
-0.000000000000000087,
0.000000000000000036
};
const cheb_series _gsl_sf_bessel_amp_phase_bth0_cs = {
bth0_data,
23,
-1, 1,
12
};
static double bm1_data[21] = {
0.1047362510931285,
0.00442443893702345,
-0.00005661639504035,
0.00000231349417339,
-0.00000017377182007,
0.00000001893209930,
-0.00000000265416023,
0.00000000044740209,
-0.00000000008691795,
0.00000000001891492,
-0.00000000000451884,
0.00000000000116765,
-0.00000000000032265,
0.00000000000009450,
-0.00000000000002913,
0.00000000000000939,
-0.00000000000000315,
0.00000000000000109,
-0.00000000000000039,
0.00000000000000014,
-0.00000000000000005,
};
const cheb_series _gsl_sf_bessel_amp_phase_bm1_cs = {
bm1_data,
20,
-1, 1,
10
};
static double bth1_data[24] = {
0.74060141026313850,
-0.004571755659637690,
0.000119818510964326,
-0.000006964561891648,
0.000000655495621447,
-0.000000084066228945,
0.000000013376886564,
-0.000000002499565654,
0.000000000529495100,
-0.000000000124135944,
0.000000000031656485,
-0.000000000008668640,
0.000000000002523758,
-0.000000000000775085,
0.000000000000249527,
-0.000000000000083773,
0.000000000000029205,
-0.000000000000010534,
0.000000000000003919,
-0.000000000000001500,
0.000000000000000589,
-0.000000000000000237,
0.000000000000000097,
-0.000000000000000040,
};
const cheb_series _gsl_sf_bessel_amp_phase_bth1_cs = {
bth1_data,
23,
-1, 1,
12
};
int
gsl_sf_bessel_asymp_Mnu_e(const double nu, const double x, double * result)
{
const double r = 2.0*nu/x;
const double r2 = r*r;
const double x2 = x*x;
const double term1 = (r2-1.0/x2)/8.0;
const double term2 = (r2-1.0/x2)*(r2-9.0/x2)*3.0/128.0;
const double Mnu2_c = 2.0/(M_PI) * (1.0 + term1 + term2);
*result = sqrt(Mnu2_c)/sqrt(x); /* will never underflow this way */
return GSL_SUCCESS;
}
int
gsl_sf_bessel_asymp_thetanu_corr_e(const double nu, const double x, double * result)
{
const double r = 2.0*nu/x;
const double r2 = r*r;
const double x2 = x*x;
const double term1 = x*(r2 - 1.0/x2)/8.0;
const double term2 = x*(r2 - 1.0/x2)*(r2 - 25.0/x2)/384.0;
*result = (-0.25*M_PI + term1 + term2);
return GSL_SUCCESS;
}
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