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- /* 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_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);
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