My gnuplot version with hypergeometric function using GNU Scientific Library
hyperg_2F1.patch
--- ./src/eval.c.orig 2016-08-12 17:06:35.250145505 -0300
+++ ./src/eval.c 2016-05-03 12:34:08.000000000 -0300
@@ -191,6 +191,7 @@
{"lambertw", f_lambertw}, /* HBB, from G.Kuhnle 20001107 */
{"airy", f_airy}, /* janert, 20090905 */
{"expint", f_expint}, /* Jim Van Zandt, 20101010 */
+ {"hyperg_2F1",f_hyperg_2F1},
#ifdef HAVE_LIBCERF
{"cerf", f_cerf}, /* complex error function */
--- ./src/specfun.c.orig 2016-08-12 17:06:35.248145450 -0300
+++ ./src/specfun.c 2016-05-03 12:20:14.000000000 -0300
@@ -49,6 +49,7 @@
#include "specfun.h"
#include "stdfn.h"
#include "util.h"
+#include "gsl/gsl_sf_hyperg.h"
#define ITMAX 200
@@ -3031,9 +3032,11 @@
extern double p1evl ( double, void *, int );
extern double sin ( double );
extern double cos ( double );
+extern double gsl_sf_hyperg_2F1( double , double, double, double);
#else
double fabs(), exp(), sqrt();
double polevl(), p1evl(), sin(), cos();
+double gsl_sf_hyperg_2F1();
#endif
int
--- ./src/standard.c.orig 2016-08-12 17:06:35.255145644 -0300
+++ ./src/standard.c 2016-05-03 14:40:24.741731493 -0300
@@ -39,6 +39,7 @@
#include "gadgets.h" /* for 'ang2rad' and 'zero' */
#include "gp_time.h" /* needed by f_tmsec() and friendsa */
#include "util.h" /* for int_error() */
+#include "gsl/gsl_sf_hyperg.h"
static double carlson_elliptic_rc(double x,double y);
static double carlson_elliptic_rf(double x,double y,double z);
@@ -57,7 +58,7 @@
static double yone __PROTO((double x));
static double rj1 __PROTO((double x));
static double ry1 __PROTO((double x));
-
+extern double gsl_sf_hyperg_2F1(double,double,double,double);
/* The bessel function approximations here are from
* "Computer Approximations"
* by Hart, Cheney et al.
@@ -841,6 +842,30 @@
}
}
+void
+f_hyperg_2F1(union argument *arg)
+{
+ struct value a1;
+ double aa,bb,cc,zz;
+
+ (void) arg; /* avoid -Wunused warning */
+ zz=real(pop(&a1));
+ cc=real(pop(&a1));
+ bb=real(pop(&a1));
+ aa=real(pop(&a1));
+// if (fabs(imag(&a1)) > zero || fabs(imag(&a2)) > zero)
+// int_error(NO_CARET, "can only do elliptic integrals of reals");
+
+ if (zz < 1.0 && zz > 0)
+ push(Gcomplex(&a1, gsl_sf_hyperg_2F1(aa,bb,cc,zz), 0.0));
+ else if (zz < 0) {
+ push(Gcomplex(&a1, pow(1-zz,-aa)*gsl_sf_hyperg_2F1(aa,cc-bb,cc,zz/(zz-1)), 0.0));
+ } else {
+ undefined=TRUE;
+ push(&a1);
+ }
+
+}
/* Terminate the autoconversion from string to numeric values */
#undef pop
--- ./src/standard.h.orig 2016-08-12 17:06:35.252145560 -0300
+++ ./src/standard.h 2016-05-03 12:37:23.000000000 -0300
@@ -93,5 +93,6 @@
void f_tmyear __PROTO((union argument *x));
void f_tmwday __PROTO((union argument *x));
void f_tmyday __PROTO((union argument *x));
+void f_hyperg_2F1 __PROTO((union argument *x));
#endif /* GNUPLOT_STANDARD_H */
