/* specfunc/bessel.h

 * 

 * 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 */

#ifndef _BESSEL_H_

#define _BESSEL_H_

#include <gsl/gsl_sf_result.h>

/* Taylor expansion for J_nu(x) or I_nu(x)

 *   sign = -1  ==> Jnu

 *   sign = +1  ==> Inu

 */

int gsl_sf_bessel_IJ_taylor_e(const double nu, const double x,

                                 const int sign,

                                 const int kmax,

                                 const double threshold,

                                 gsl_sf_result * result

                                 );

int gsl_sf_bessel_Jnu_asympx_e(const double nu, const double x, gsl_sf_result * result);

int gsl_sf_bessel_Ynu_asympx_e(const double nu, const double x, gsl_sf_result * result);

int gsl_sf_bessel_Jnupos_e(const double nu, const double x, gsl_sf_result * result);

int gsl_sf_bessel_Ynupos_e(const double nu, const double x, gsl_sf_result * result);

int gsl_sf_bessel_Inu_scaled_asympx_e(const double nu, const double x, gsl_sf_result * result);

int gsl_sf_bessel_Knu_scaled_asympx_e(const double nu, const double x, gsl_sf_result * result);

int gsl_sf_bessel_Inu_scaled_asymp_unif_e(const double nu, const double x, gsl_sf_result * result);

int gsl_sf_bessel_Knu_scaled_asymp_unif_e(const double nu, const double x, gsl_sf_result * result);

/* ratio = J_{nu+1}(x) / J_nu(x)

 * sgn   = sgn(J_nu(x))

 */

int

gsl_sf_bessel_J_CF1(const double nu, const double x, double * ratio, double * sgn);

/* ratio = I_{nu+1}(x) / I_nu(x)

 */

int

gsl_sf_bessel_I_CF1_ser(const double nu, const double x, double * ratio);

/* Evaluate the Steed method continued fraction CF2 for

 *

 * (J' + i Y')/(J + i Y) := P + i Q

 */

int

gsl_sf_bessel_JY_steed_CF2(const double nu, const double x,

                           double * P, double * Q);

int

gsl_sf_bessel_JY_mu_restricted(const double mu, const double x,

                               gsl_sf_result * Jmu, gsl_sf_result * Jmup1,

                               gsl_sf_result * Ymu, gsl_sf_result * Ymup1);

int

gsl_sf_bessel_K_scaled_steed_temme_CF2(const double nu, const double x,

                                       double * K_nu, double * K_nup1,

                                       double * Kp_nu);

/* These are of use in calculating the oscillating

 * Bessel functions.

 *   cos(y - pi/4 + eps)

 *   sin(y - pi/4 + eps)

 */

int gsl_sf_bessel_cos_pi4_e(double y, double eps, gsl_sf_result * result);

int gsl_sf_bessel_sin_pi4_e(double y, double eps, gsl_sf_result * result);

#endif /* !_BESSEL_H_ */