1 files changed, 112 insertions, 0 deletions
diff --git a/gsl-1.9/specfunc/gsl_sf_ellint.h b/gsl-1.9/specfunc/gsl_sf_ellint.h
new file mode 100644
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+++ b/gsl-1.9/specfunc/gsl_sf_ellint.h
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+/* specfunc/gsl_sf_ellint.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 */
+
+#ifndef __GSL_SF_ELLINT_H__
+#define __GSL_SF_ELLINT_H__
+
+#include <gsl/gsl_mode.h>
+#include <gsl/gsl_sf_result.h>
+
+#undef __BEGIN_DECLS
+#undef __END_DECLS
+#ifdef __cplusplus
+# define __BEGIN_DECLS extern "C" {
+# define __END_DECLS }
+#else
+# define __BEGIN_DECLS /* empty */
+# define __END_DECLS /* empty */
+#endif
+
+__BEGIN_DECLS
+
+
+/* Legendre form of complete elliptic integrals
+ *
+ * K(k) = Integral[1/Sqrt[1 - k^2 Sin[t]^2], {t, 0, Pi/2}]
+ * E(k) = Integral[  Sqrt[1 - k^2 Sin[t]^2], {t, 0, Pi/2}]
+ *
+ * exceptions: GSL_EDOM
+ */
+int gsl_sf_ellint_Kcomp_e(double k, gsl_mode_t mode, gsl_sf_result * result);
+double gsl_sf_ellint_Kcomp(double k, gsl_mode_t mode);
+
+int gsl_sf_ellint_Ecomp_e(double k, gsl_mode_t mode, gsl_sf_result * result);
+double gsl_sf_ellint_Ecomp(double k, gsl_mode_t mode);
+
+int gsl_sf_ellint_Pcomp_e(double k, double n, gsl_mode_t mode, gsl_sf_result * result);
+double gsl_sf_ellint_Pcomp(double k, double n, gsl_mode_t mode);
+
+int gsl_sf_ellint_Dcomp_e(double k, gsl_mode_t mode, gsl_sf_result * result);
+double gsl_sf_ellint_Dcomp(double k, gsl_mode_t mode);
+
+
+/* Legendre form of incomplete elliptic integrals
+ *
+ * F(phi,k)   = Integral[1/Sqrt[1 - k^2 Sin[t]^2], {t, 0, phi}]
+ * E(phi,k)   = Integral[  Sqrt[1 - k^2 Sin[t]^2], {t, 0, phi}]
+ * P(phi,k,n) = Integral[(1 + n Sin[t]^2)^(-1)/Sqrt[1 - k^2 Sin[t]^2], {t, 0, phi}]
+ * D(phi,k,n) = R_D(1-Sin[phi]^2, 1-k^2 Sin[phi]^2, 1.0)
+ *
+ * F: [Carlson, Numerische Mathematik 33 (1979) 1, (4.1)]
+ * E: [Carlson, ", (4.2)]
+ * P: [Carlson, ", (4.3)]
+ * D: [Carlson, ", (4.4)]
+ *
+ * exceptions: GSL_EDOM
+ */
+int gsl_sf_ellint_F_e(double phi, double k, gsl_mode_t mode, gsl_sf_result * result);
+double gsl_sf_ellint_F(double phi, double k, gsl_mode_t mode);
+
+int gsl_sf_ellint_E_e(double phi, double k, gsl_mode_t mode, gsl_sf_result * result);
+double gsl_sf_ellint_E(double phi, double k, gsl_mode_t mode);
+
+int gsl_sf_ellint_P_e(double phi, double k, double n, gsl_mode_t mode, gsl_sf_result * result);
+double gsl_sf_ellint_P(double phi, double k, double n, gsl_mode_t mode);
+
+int gsl_sf_ellint_D_e(double phi, double k, double n, gsl_mode_t mode, gsl_sf_result * result);
+double gsl_sf_ellint_D(double phi, double k, double n, gsl_mode_t mode);
+
+
+/* Carlson's symmetric basis of functions
+ *
+ * RC(x,y)   = 1/2 Integral[(t+x)^(-1/2) (t+y)^(-1)], {t,0,Inf}]
+ * RD(x,y,z) = 3/2 Integral[(t+x)^(-1/2) (t+y)^(-1/2) (t+z)^(-3/2), {t,0,Inf}]
+ * RF(x,y,z) = 1/2 Integral[(t+x)^(-1/2) (t+y)^(-1/2) (t+z)^(-1/2), {t,0,Inf}]
+ * RJ(x,y,z,p) = 3/2 Integral[(t+x)^(-1/2) (t+y)^(-1/2) (t+z)^(-1/2) (t+p)^(-1), {t,0,Inf}]
+ *
+ * exceptions: GSL_EDOM
+ */
+int gsl_sf_ellint_RC_e(double x, double y, gsl_mode_t mode, gsl_sf_result * result);
+double gsl_sf_ellint_RC(double x, double y, gsl_mode_t mode);
+
+int gsl_sf_ellint_RD_e(double x, double y, double z, gsl_mode_t mode, gsl_sf_result * result);
+double gsl_sf_ellint_RD(double x, double y, double z, gsl_mode_t mode);
+
+int gsl_sf_ellint_RF_e(double x, double y, double z, gsl_mode_t mode, gsl_sf_result * result);
+double gsl_sf_ellint_RF(double x, double y, double z, gsl_mode_t mode);
+
+int gsl_sf_ellint_RJ_e(double x, double y, double z, double p, gsl_mode_t mode, gsl_sf_result * result);
+double gsl_sf_ellint_RJ(double x, double y, double z, double p, gsl_mode_t mode);
+
+
+__END_DECLS
+
+#endif /* __GSL_SF_ELLINT_H__ */