/* specfunc/bessel_Yn.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_gamma.h>

#include <gsl/gsl_sf_psi.h>

#include <gsl/gsl_sf_bessel.h>

#include "error.h"

#include "bessel.h"

#include "bessel_amp_phase.h"

#include "bessel_olver.h"

/*-*-*-*-*-*-*-*-*-*-*-* Private Section *-*-*-*-*-*-*-*-*-*-*-*/

/* assumes n >= 1 */

static int bessel_Yn_small_x(const int n, const double x, gsl_sf_result * result)

{

  int k;

  double y = 0.25 * x * x;

  double ln_x_2 = log(0.5*x);

  gsl_sf_result ln_nm1_fact;

  double k_term;

  double term1, sum1, ln_pre1;

  double term2, sum2, pre2;

  gsl_sf_lnfact_e((unsigned int)(n-1), &ln_nm1_fact);

  ln_pre1 = -n*ln_x_2 + ln_nm1_fact.val;

  if(ln_pre1 > GSL_LOG_DBL_MAX - 3.0) GSL_ERROR ("error", GSL_EOVRFLW);

  sum1 = 1.0;

  k_term = 1.0;

  for(k=1; k<=n-1; k++) {

    k_term *= y/(k * (n-k));

    sum1 += k_term;

  }

  term1 = -exp(ln_pre1) * sum1 / M_PI;

  pre2 = -exp(n*ln_x_2) / M_PI;

  if(fabs(pre2) > 0.0) {

    const int KMAX = 20;

    gsl_sf_result psi_n;

    gsl_sf_result npk_fact;

    double yk = 1.0;

    double k_fact  = 1.0;

    double psi_kp1 = -M_EULER;

    double psi_npkp1;

    gsl_sf_psi_int_e(n, &psi_n);

    gsl_sf_fact_e((unsigned int)n, &npk_fact);

    psi_npkp1 = psi_n.val + 1.0/n;

    sum2 = (psi_kp1 + psi_npkp1 - 2.0*ln_x_2)/npk_fact.val;

    for(k=1; k

      psi_kp1   += 1./k;

      psi_npkp1 += 1./(n+k);

      k_fact   *= k;

      npk_fact.val *= n+k;

      yk *= -y;

      k_term = yk*(psi_kp1 + psi_npkp1 - 2.0*ln_x_2)/(k_fact*npk_fact.val);

      sum2 += k_term;

    }

    term2 = pre2 * sum2;

  }

  else {

    term2 = 0.0;

  }

  result->val  = term1 + term2;

  result->err  = GSL_DBL_EPSILON * (fabs(ln_pre1)*fabs(term1) + fabs(term2));

  result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val);

  return GSL_SUCCESS;

}

/*-*-*-*-*-*-*-*-*-*-*-* Functions with Error Codes *-*-*-*-*-*-*-*-*-*-*-*/

int

gsl_sf_bessel_Yn_e(int n, const double x, gsl_sf_result * result)

{

  int sign = 1;

  if(n < 0) {

    /* reduce to case n >= 0 */

    n = -n;

    if(GSL_IS_ODD(n)) sign = -1;

  }

  /* CHECK_POINTER(result) */

  if(n == 0) {

    int status = gsl_sf_bessel_Y0_e(x, result);

    result->val *= sign;

    return status;

  }

  else if(n == 1) {

    int status = gsl_sf_bessel_Y1_e(x, result);

    result->val *= sign;

    return status;

  }

  else {

    if(x <= 0.0) {

      DOMAIN_ERROR(result);

    }

    if(x < 5.0) {

      int status = bessel_Yn_small_x(n, x, result);

      result->val *= sign;

      return status;

    }

    else if(GSL_ROOT3_DBL_EPSILON * x > (n*n + 1.0)) {

      int status = gsl_sf_bessel_Ynu_asympx_e((double)n, x, result);

      result->val *= sign;

      return status;

    }

    else if(n > 50) {

      int status = gsl_sf_bessel_Ynu_asymp_Olver_e((double)n, x, result);

      result->val *= sign;

      return status;

    }

    else {

      double two_over_x = 2.0/x;

      gsl_sf_result r_by;

      gsl_sf_result r_bym;

      int stat_1 = gsl_sf_bessel_Y1_e(x, &r_by);

      int stat_0 = gsl_sf_bessel_Y0_e(x, &r_bym);

      double bym = r_bym.val;

      double by  = r_by.val;

      double byp;

      int j;

      for(j=1; j

        byp = j*two_over_x*by - bym;

        bym = by;

        by  = byp;

      }

      result->val  = sign * by;

      result->err  = fabs(result->val) * (fabs(r_by.err/r_by.val) + fabs(r_bym.err/r_bym.val));

      result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val);

      return GSL_ERROR_SELECT_2(stat_1, stat_0);

    }

  }

}

int

gsl_sf_bessel_Yn_array(const int nmin, const int nmax, const double x, double * result_array)

{

  /* CHECK_POINTER(result_array) */

  if(nmin < 0 || nmax < nmin || x <= 0.0) {

    int j;

    for(j=0; j<=nmax-nmin; j++) result_array[j] = 0.0;

    GSL_ERROR ("error", GSL_EDOM);

  }

  else {

    gsl_sf_result r_Ynm1;

    gsl_sf_result r_Yn;

    int stat_nm1 = gsl_sf_bessel_Yn_e(nmin,   x, &r_Ynm1);

    int stat_n   = gsl_sf_bessel_Yn_e(nmin+1, x, &r_Yn);

    double Ynp1;

    double Yn   = r_Yn.val;

    double Ynm1 = r_Ynm1.val;

    int n;

    int stat = GSL_ERROR_SELECT_2(stat_nm1, stat_n);

    if(stat == GSL_SUCCESS) {

      for(n=nmin+1; n<=nmax+1; n++) {

        result_array[n-nmin-1] = Ynm1;

        Ynp1 = -Ynm1 + 2.0*n/x * Yn;

        Ynm1 = Yn;

        Yn   = Ynp1;

      }

    }

    else {

      for(n=nmin; n<=nmax; n++) {

        result_array[n-nmin] = 0.0;

      }

    }

    return stat;

  }

}

/*-*-*-*-*-*-*-*-*-* Functions w/ Natural Prototypes *-*-*-*-*-*-*-*-*-*-*/

#include "eval.h"

double gsl_sf_bessel_Yn(const int n, const double x)

{

  EVAL_RESULT(gsl_sf_bessel_Yn_e(n, x, &result));

}