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/*
Copyright (C) 2014 Fredrik Johansson
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_pfq_bound_factor(mag_t C,
acb_srcptr a, slong p, acb_srcptr b, slong q, const acb_t z, ulong n)
{
mag_t t, u;
acb_t w;
slong i;
if (p > q)
{
mag_inf(C);
return;
}
mag_init(t);
mag_init(u);
acb_init(w);
acb_get_mag(C, z);
for (i = 0; i < q; i++)
{
acb_add_ui(w, b + i, n, MAG_BITS);
if (arb_is_positive(acb_realref(w)))
{
acb_get_mag_lower(u, w);
if (i < p)
{
acb_sub(w, a + i, b + i, MAG_BITS);
acb_get_mag(t, w);
mag_div(t, t, u);
mag_one(u);
mag_add(t, t, u);
mag_mul(C, C, t);
}
else
{
mag_div(C, C, u);
}
}
else
{
mag_inf(C);
}
}
mag_one(t);
mag_sub_lower(u, t, C);
if (mag_is_zero(u))
mag_inf(C);
else
mag_div(C, t, u);
mag_clear(t);
mag_clear(u);
acb_clear(w);
}