/* 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);