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/*
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_pfq_series_sum_forward(acb_poly_t s, acb_poly_t t,
const acb_poly_struct * a, slong p,
const acb_poly_struct * b, slong q,
const acb_poly_t z, int regularized,
slong n, slong len, slong prec)
{
acb_poly_t u, v;
acb_poly_t tmp;
slong k, i;
acb_poly_init(u);
acb_poly_init(v);
acb_poly_init(tmp);
if (!regularized)
{
acb_poly_zero(s);
acb_poly_one(t);
for (k = 0; k < n && acb_poly_length(t) != 0; k++)
{
acb_poly_add(s, s, t, prec);
if (p > 0)
{
acb_poly_add_si(u, a, k, prec);
for (i = 1; i < p; i++)
{
acb_poly_add_si(v, a + i, k, prec);
acb_poly_mullow(u, u, v, len, prec);
}
acb_poly_mullow(t, t, u, len, prec);
}
if (q > 0)
{
acb_poly_add_si(u, b, k, prec);
for (i = 1; i < q; i++)
{
acb_poly_add_si(v, b + i, k, prec);
acb_poly_mullow(u, u, v, len, prec);
}
acb_poly_div_series(t, t, u, len, prec);
}
acb_poly_mullow(t, t, z, len, prec);
}
}
else
{
acb_poly_zero(s);
if (q == 0)
acb_poly_one(t);
for (i = 0; i < q; i++)
{
if (i == 0)
{
acb_poly_rgamma_series(t, b + i, len, prec);
}
else
{
acb_poly_rgamma_series(u, b + i, len, prec);
acb_poly_mullow(tmp, t, u, len, prec);
acb_poly_swap(tmp, t);
}
}
for (k = 0; k < n; k++)
{
acb_poly_add(s, s, t, prec);
if (p > 0)
{
acb_poly_add_si(u, a, k, prec);
for (i = 1; i < p; i++)
{
acb_poly_add_si(v, a + i, k, prec);
acb_poly_mullow(tmp, u, v, len, prec);
acb_poly_swap(tmp, u);
}
acb_poly_mullow(tmp, t, u, len, prec);
acb_poly_swap(tmp, t);
}
if (q > 0)
{
acb_poly_add_si(u, b, k, prec);
for (i = 1; i < q; i++)
{
acb_poly_add_si(v, b + i, k, prec);
acb_poly_mullow(tmp, u, v, len, prec);
acb_poly_swap(tmp, u);
}
if (acb_poly_length(u) > 0 && !acb_contains_zero(u->coeffs))
{
acb_poly_div_series(tmp, t, u, len, prec);
acb_poly_mullow(t, tmp, z, len, prec);
}
else
{
/* compute term from scratch */
acb_poly_one(t);
for (i = 0; i < p; i++)
{
acb_poly_rising_ui_series(v, a + i, k + 1, len, prec);
acb_poly_mullow(t, t, v, len, prec);
}
for (i = 0; i < q; i++)
{
acb_poly_add_si(v, b + i, k + 1, prec);
acb_poly_rgamma_series(v, v, len, prec);
acb_poly_mullow(t, t, v, len, prec);
}
acb_poly_pow_ui_trunc_binexp(v, z, k + 1, len, prec);
acb_poly_mullow(t, t, v, len, prec);
}
}
else
{
acb_poly_mullow(tmp, t, z, len, prec);
acb_poly_swap(tmp, t);
}
}
}
acb_poly_clear(u);
acb_poly_clear(v);
acb_poly_clear(tmp);
}
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