| /* 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 2 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); |
