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/* specfunc/gegenbauer.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_gegenbauer.h>
#include "error.h"
/* See: [Thompson, Atlas for Computing Mathematical Functions] */
int
gsl_sf_gegenpoly_1_e(double lambda, double x, gsl_sf_result * result)
{
/* CHECK_POINTER(result) */
if(lambda == 0.0) {
result->val = 2.0*x;
result->err = 2.0 * GSL_DBL_EPSILON * fabs(result->val);
return GSL_SUCCESS;
}
else {
result->val = 2.0*lambda*x;
result->err = 4.0 * GSL_DBL_EPSILON * fabs(result->val);
return GSL_SUCCESS;
}
}
int
gsl_sf_gegenpoly_2_e(double lambda, double x, gsl_sf_result * result)
{
/* CHECK_POINTER(result) */
if(lambda == 0.0) {
const double txx = 2.0*x*x;
result->val = -1.0 + txx;
result->err = 2.0 * GSL_DBL_EPSILON * fabs(txx);
result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val);
return GSL_SUCCESS;
}
else {
result->val = lambda*(-1.0 + 2.0*(1.0+lambda)*x*x);
result->err = GSL_DBL_EPSILON * (2.0 * fabs(result->val) + fabs(lambda));
return GSL_SUCCESS;
}
}
int
gsl_sf_gegenpoly_3_e(double lambda, double x, gsl_sf_result * result)
{
/* CHECK_POINTER(result) */
if(lambda == 0.0) {
result->val = x*(-2.0 + 4.0/3.0*x*x);
result->err = GSL_DBL_EPSILON * (2.0 * fabs(result->val) + fabs(x));
return GSL_SUCCESS;
}
else {
double c = 4.0 + lambda*(6.0 + 2.0*lambda);
result->val = 2.0*lambda * x * ( -1.0 - lambda + c*x*x/3.0 );
result->err = GSL_DBL_EPSILON * (2.0 * fabs(result->val) + fabs(lambda * x));
return GSL_SUCCESS;
}
}
int
gsl_sf_gegenpoly_n_e(int n, double lambda, double x, gsl_sf_result * result)
{
/* CHECK_POINTER(result) */
if(lambda <= -0.5 || n < 0) {
DOMAIN_ERROR(result);
}
else if(n == 0) {
result->val = 1.0;
result->err = 0.0;
return GSL_SUCCESS;
}
else if(n == 1) {
return gsl_sf_gegenpoly_1_e(lambda, x, result);
}
else if(n == 2) {
return gsl_sf_gegenpoly_2_e(lambda, x, result);
}
else if(n == 3) {
return gsl_sf_gegenpoly_3_e(lambda, x, result);
}
else {
if(lambda == 0.0 && (x >= -1.0 || x <= 1.0)) {
/* 2 T_n(x)/n */
const double z = n * acos(x);
result->val = 2.0 * cos(z) / n;
result->err = 2.0 * GSL_DBL_EPSILON * fabs(z * result->val);
return GSL_SUCCESS;
}
else {
int k;
gsl_sf_result g2;
gsl_sf_result g3;
int stat_g2 = gsl_sf_gegenpoly_2_e(lambda, x, &g2);
int stat_g3 = gsl_sf_gegenpoly_3_e(lambda, x, &g3);
int stat_g = GSL_ERROR_SELECT_2(stat_g2, stat_g3);
double gkm2 = g2.val;
double gkm1 = g3.val;
double gk = 0.0;
for(k=4; k<=n; k++) {
gk = (2.0*(k+lambda-1.0)*x*gkm1 - (k+2.0*lambda-2.0)*gkm2) / k;
gkm2 = gkm1;
gkm1 = gk;
}
result->val = gk;
result->err = 2.0 * GSL_DBL_EPSILON * 0.5 * n * fabs(gk);
return stat_g;
}
}
}
int
gsl_sf_gegenpoly_array(int nmax, double lambda, double x, double * result_array)
{
int k;
/* CHECK_POINTER(result_array) */
if(lambda <= -0.5 || nmax < 0) {
GSL_ERROR("domain error", GSL_EDOM);
}
/* n == 0 */
result_array[0] = 1.0;
if(nmax == 0) return GSL_SUCCESS;
/* n == 1 */
if(lambda == 0.0)
result_array[1] = 2.0*x;
else
result_array[1] = 2.0*lambda*x;
/* n <= nmax */
for(k=2; k<=nmax; k++) {
double term1 = 2.0*(k+lambda-1.0) * x * result_array[k-1];
double term2 = (k+2.0*lambda-2.0) * result_array[k-2];
result_array[k] = (term1 - term2) / k;
}
return GSL_SUCCESS;
}
/*-*-*-*-*-*-*-*-*-* Functions w/ Natural Prototypes *-*-*-*-*-*-*-*-*-*-*/
#include "eval.h"
double gsl_sf_gegenpoly_1(double lambda, double x)
{
EVAL_RESULT(gsl_sf_gegenpoly_1_e(lambda, x, &result));
}
double gsl_sf_gegenpoly_2(double lambda, double x)
{
EVAL_RESULT(gsl_sf_gegenpoly_2_e(lambda, x, &result));
}
double gsl_sf_gegenpoly_3(double lambda, double x)
{
EVAL_RESULT(gsl_sf_gegenpoly_3_e(lambda, x, &result));
}
double gsl_sf_gegenpoly_n(int n, double lambda, double x)
{
EVAL_RESULT(gsl_sf_gegenpoly_n_e(n, lambda, x, &result));
}
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