arb/acb_hypgeom/gamma_lower.c
2016-04-15 20:34:50 -04:00

119 lines
3 KiB
C

/*=============================================================================
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) 2016 Arb authors
******************************************************************************/
#include "acb_hypgeom.h"
void
acb_hypgeom_gamma_lower_1f1a(acb_t res, const acb_t s,
const acb_t z, int regularized, slong prec)
{
acb_t a, w;
acb_struct b[2];
acb_init(a);
acb_init(b);
acb_init(b + 1);
acb_init(w);
acb_set(a, s);
acb_add_ui(b, s, 1, prec);
acb_one(b + 1);
acb_neg(w, z);
/* res = 1F1(s, s+1, -z) / s */
acb_hypgeom_pfq_direct(res, a, 1, b, 2, w, -1, prec);
acb_div(res, res, s, prec);
if (regularized == 0)
{
acb_pow(a, z, s, prec);
acb_mul(res, res, a, prec);
}
else if (regularized == 1)
{
acb_pow(a, z, s, prec);
acb_mul(res, res, a, prec);
acb_rgamma(a, s, prec);
acb_mul(res, res, a, prec);
}
acb_clear(a);
acb_clear(b);
acb_clear(b + 1);
acb_clear(w);
}
void
acb_hypgeom_gamma_lower_1f1b(acb_t res, const acb_t s,
const acb_t z, int regularized, slong prec)
{
acb_t a, b;
acb_init(a);
acb_init(b);
acb_add_ui(b, s, 1, prec);
acb_hypgeom_pfq_direct(res, NULL, 0, b, 1, z, -1, prec);
acb_div(res, res, s, prec);
acb_neg(a, z);
acb_exp(a, a, prec);
acb_mul(res, res, a, prec);
if (regularized == 0)
{
acb_pow(a, z, s, prec);
acb_mul(res, res, a, prec);
}
else if (regularized == 1)
{
acb_pow(a, z, s, prec);
acb_mul(res, res, a, prec);
acb_rgamma(a, s, prec);
acb_mul(res, res, a, prec);
}
acb_clear(a);
acb_clear(b);
}
void
acb_hypgeom_gamma_lower(acb_t res, const acb_t s, const acb_t z, int regularized, slong prec)
{
if (!acb_is_finite(s) || !acb_is_finite(z))
{
acb_indeterminate(res);
return;
}
/* todo: handle the case where z is zero */
/* todo: handle the case where s is an integer */
if (arf_sgn(arb_midref(acb_realref(z))) > 0)
acb_hypgeom_gamma_lower_1f1b(res, s, z, regularized, prec);
else
acb_hypgeom_gamma_lower_1f1a(res, s, z, regularized, prec);
}