1 files changed, 72 insertions, 0 deletions
diff --git a/gsl-1.9/specfunc/legendre.h b/gsl-1.9/specfunc/legendre.h
new file mode 100644
index 0000000..e82c0cf
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+++ b/gsl-1.9/specfunc/legendre.h
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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 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);