arb/acb_hypgeom/gamma_lower.c

70 lines
2 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(acb_t res, const acb_t s, const acb_t z, int regularized, slong prec)
{
acb_t s1, nz, t;
if (!acb_is_finite(s) || !acb_is_finite(z))
{
acb_indeterminate(res);
return;
}
acb_init(s1);
acb_init(nz);
acb_init(t);
acb_add_ui(s1, s, 1, prec);
acb_neg(nz, z);
if (regularized == 0)
{
/* \gamma(s, z) = s^-1 z^s 1F1(s, 1+s, -z) */
acb_hypgeom_m(res, s, s1, nz, 0, prec);
acb_pow(t, z, s, prec);
acb_mul(res, res, t, prec);
acb_div(res, res, s, prec);
}
else if (regularized == 1)
{
/* P(s, z) = z^s \gamma^{*}(s, z) */
acb_hypgeom_m(res, s, s1, nz, 1, prec);
acb_pow(t, z, s, prec);
acb_mul(res, res, t, prec);
}
else if (regularized == 2)
{
/* \gamma^{*}(s, z) */
acb_hypgeom_m(res, s, s1, nz, 1, prec);
}
acb_clear(s1);
acb_clear(nz);
acb_clear(t);
}