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/*
Copyright (C) 2016 Arb authors
This file is part of FLINT.
FLINT 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 3 of the License, or
(at your option) any later version. See <https://www.gnu.org/licenses/>.
*/
#include "acb.h"
#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, u;
if (!acb_is_finite(s) || !acb_is_finite(z))
{
acb_indeterminate(res);
return;
}
acb_init(s1);
acb_init(nz);
acb_init(t);
acb_init(u);
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(u, s, s1, nz, 0, prec);
acb_pow(t, z, s, prec);
acb_mul(u, u, t, prec);
acb_div(res, u, s, prec);
}
else if (regularized == 1)
{
/* P(s, z) = z^s \gamma^{*}(s, z) */
acb_hypgeom_m(u, s, s1, nz, 1, prec);
acb_pow(t, z, s, prec);
acb_mul(res, u, 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);
acb_clear(u);
}