arb/acb_hypgeom/2f1_corner.c
2016-04-26 17:20:05 +02:00

59 lines
1.7 KiB
C

/*
Copyright (C) 2015 Fredrik Johansson
This file is part of Arb.
Arb is free software: you can redistribute it and/or modify it under
the terms of the GNU Lesser General Public License (LGPL) as published
by the Free Software Foundation; either version 2.1 of the License, or
(at your option) any later version. See <http://www.gnu.org/licenses/>.
*/
#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, slong 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 */
#if 0
acb_set_d_d(z1, 0.5, upper ? 0.5 : -0.5);
acb_set_d_d(z2, 0.5, upper ? 0.75 : -0.75);
#else
acb_set_d_d(z1, 0.375, upper ? 0.625 : -0.625);
acb_set_d_d(z2, 0.5, upper ? 0.8125 : -0.8125);
#endif
acb_hypgeom_2f1_direct(f1, a, b, c, z1, regularized, prec);
acb_hypgeom_2f1_direct(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);
}