/* 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 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 */

#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));

}