/* specfunc/legendre.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 */

/* Declare private but non-local support functions

 * used in various Legendre function evaluations.

 */

#include <gsl/gsl_sf_result.h>

/* Large negative mu asymptotic

 * P^{-mu}_{-1/2 + I tau}, mu -> Inf

 * |x| < 1

 */

int

gsl_sf_conicalP_xlt1_large_neg_mu_e(double mu, double tau, double x,

                                       gsl_sf_result * result, double * ln_multiplier);

/* Large tau uniform asymptotics

 * P^{-mu}_{-1/2 + I tau}, tau -> Inf

 * 1 < x

 */

int

gsl_sf_conicalP_xgt1_neg_mu_largetau_e(const double mu, const double tau,

                                          const double x, double acosh_x,

                                          gsl_sf_result * result, double * ln_multiplier);

/* Large tau uniform asymptotics

 * P^{-mu}_{-1/2 + I tau}, tau -> Inf 

 * -1 < x < 1

 */

int

gsl_sf_conicalP_xlt1_neg_mu_largetau_e(const double mu, const double tau,

                                          const double x, const double acos_x,

                                          gsl_sf_result * result, double * ln_multiplier);

/* P^{mu}_{-1/2 + I tau}

 * x->Inf

 *

 *  * This is effective to precision EPS for

 *

 *    (mu^2 + tau^2)/((1 + tau^2)^(1/2) x^2) < EPS^{1/3}

 *

 * since it goes only to a fixed order, based on the

 * representation in terms of hypegeometric functions

 * of argument 1/x^2.

 * [Zhurina+Karmazina, (3.8)]

 */

int

gsl_sf_conicalP_large_x_e(const double mu, const double tau, const double x,

                             gsl_sf_result * result, double * ln_multiplier);