code for 2F1 in the exp(pi i/3) corner case

acb_hypgeom.h

@@ -150,6 +150,8 @@ void acb_hypgeom_2f1_direct(acb_t res, const acb_t a, const acb_t b, const acb_t
 void acb_hypgeom_2f1_pfaff(acb_t res, const acb_t a, const acb_t b, const acb_t c, const acb_t z, int regularized, long prec);
 void acb_hypgeom_2f1_inf(acb_t res, const acb_t a, const acb_t b, const acb_t c, const acb_t z, int regularized, long prec);
 void acb_hypgeom_2f1_inf_limit(acb_t res, const acb_t a, const acb_t b, const acb_t c, const acb_t z, int regularized, long prec);
+void acb_hypgeom_2f1_corner(acb_t res, const acb_t a, const acb_t b, const acb_t c, const acb_t z, int regularized, long prec);
+
 void acb_hypgeom_2f1(acb_t res, const acb_t a, const acb_t b, const acb_t c, const acb_t z, int regularized, long prec);
 
 #ifdef __cplusplus

acb_hypgeom/2f1_corner.c

@@ -0,0 +1,67 @@
+/*=============================================================================
+
+    This file is part of ARB.
+
+    ARB 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.
+
+    ARB 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 ARB; if not, write to the Free Software
+    Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
+
+=============================================================================*/
+/******************************************************************************
+
+    Copyright (C) 2015 Fredrik Johansson
+
+******************************************************************************/
+
+#include "acb_hypgeom.h"
+
+void
+acb_hypgeom_2f1_corner(acb_t res, const acb_t a, const acb_t b,
+    const acb_t c, const acb_t z, int regularized, long prec)
+{
+    acb_t aa, bb, cc, z1, z2, f1, f2;
+    int upper;
+
+    acb_init(aa); acb_init(bb); acb_init(cc);
+    acb_init(z1); acb_init(z2); acb_init(f1); acb_init(f2);
+
+    acb_add_ui(aa, a, 1, prec);
+    acb_add_ui(bb, b, 1, prec);
+    acb_add_ui(cc, c, 1, prec);
+
+    upper = arb_is_positive(acb_imagref(z));
+
+    /* 0 -> 0.5 +/- 0.5i -> 0.5 +/- 0.75i -> z */
+    acb_set_d_d(z1, 0.5, upper ? 0.5 : -0.5);
+    acb_set_d_d(z2, 0.5, upper ? 0.75 : -0.75);
+
+    acb_hypgeom_2f1(f1, a, b, c, z1, regularized, prec);
+    acb_hypgeom_2f1(f2, aa, bb, cc, z1, regularized, prec);
+    acb_mul(f2, f2, a, prec);
+    acb_mul(f2, f2, b, prec);
+    if (!regularized)
+        acb_div(f2, f2, c, prec);
+
+    acb_hypgeom_2f1_continuation(f1, f2, a, b, c, z1, z2, f1, f2, prec);
+
+    acb_set(z1, z2);
+    acb_set(z2, z);
+
+    acb_hypgeom_2f1_continuation(f1, f2, a, b, c, z1, z2, f1, f2, prec);
+
+    acb_set(res, f1);
+
+    acb_clear(aa); acb_clear(bb); acb_clear(cc);
+    acb_clear(z1); acb_clear(z2); acb_clear(f1); acb_clear(f2);
+}
+

acb_hypgeom/test/t-2f1.c

@@ -68,8 +68,8 @@ int main()
         reg1 = n_randint(state, 2);
         reg2 = n_randint(state, 2);
 
-        alg1 = n_randint(state, 4);
-        alg2 = n_randint(state, 4);
+        alg1 = n_randint(state, 5);
+        alg2 = n_randint(state, 5);
 
         switch (alg1)
         {
@@ -82,6 +82,9 @@ int main()
             case 2:
                 acb_hypgeom_2f1_inf(w1, a, b, c, z, reg1, prec1);
                 break;
+            case 3:
+                acb_hypgeom_2f1_corner(w1, a, b, c, z, reg1, prec1);
+                break;
             default:
                 acb_hypgeom_2f1(w1, a, b, c, z, reg1, prec1);
         }
@@ -97,7 +100,7 @@ int main()
             case 2:
                 acb_hypgeom_2f1_inf(w2, a, b, c, z, reg2, prec2);
                 break;
-            default:
+            default:  /* favor this */
                 acb_hypgeom_2f1(w2, a, b, c, z, reg2, prec2);
         }