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/*
Copyright (C) 2016 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"
static int
_acb_vec_maybe_nonpositive_int(acb_srcptr b, slong q)
{
slong i;
for (i = 0; i < q; i++)
if (!arb_is_positive(acb_realref(b + i)) && acb_contains_int(b + i))
return 1;
return 0;
}
void
acb_hypgeom_pfq(acb_t res, acb_srcptr a, slong p,
acb_srcptr b, slong q, const acb_t z, int regularized, slong prec)
{
if (p == 0 && q == 0)
{
acb_exp(res, z, prec);
}
else if (p == 1 && q == 0)
{
acb_t t;
acb_init(t);
acb_neg(t, a);
acb_sub_ui(res, z, 1, prec);
acb_neg(res, res);
acb_pow(res, res, t, prec);
acb_clear(t);
}
else if (p == 0 && q == 1)
{
acb_hypgeom_0f1(res, b, z, regularized, prec);
}
else if (p == 1 && q == 1)
{
acb_hypgeom_m(res, a, b, z, regularized, prec);
}
else if (p == 2 && q == 1)
{
acb_hypgeom_2f1(res, a, a + 1, b, z, regularized, prec);
}
else if (regularized && _acb_vec_maybe_nonpositive_int(b, q))
{
/* todo: implement regularized sum without using polynomials */
acb_poly_struct * tmp;
slong i;
tmp = flint_malloc(sizeof(acb_poly_struct) * (p + q + 2));
for (i = 0; i < p + q + 2; i++)
acb_poly_init(tmp + i);
for (i = 0; i < p; i++)
acb_poly_set_acb(tmp + i, a + i);
for (i = 0; i < q; i++)
acb_poly_set_acb(tmp + p + i, b + i);
acb_poly_one(tmp + p + q);
acb_poly_set_acb(tmp + p + q + 1, z);
acb_hypgeom_pfq_series_direct(tmp, tmp, p, tmp + p, q + 1,
tmp + p + q + 1, regularized, -1, 1, prec);
acb_poly_get_coeff_acb(res, tmp, 0);
for (i = 0; i < p + q + 2; i++)
acb_poly_clear(tmp + i);
flint_free(tmp);
}
else
{
acb_ptr tmp;
slong i, j, alloc = 0;
/* check if we can remove a '1' from the upper parameters */
for (i = 0; i < p; i++)
{
if (acb_is_one(a + i))
{
alloc = p;
tmp = _acb_vec_init(alloc);
for (j = 0; j < p - 1; j++)
acb_set(tmp + 1 + j, a + j + (j >= i));
acb_hypgeom_pfq_direct(tmp, tmp + 1, p - 1, b, q, z, -1, prec);
break;
}
}
if (alloc == 0)
{
alloc = q + 2;
tmp = _acb_vec_init(alloc);
for (j = 0; j < q; j++)
acb_set(tmp + 1 + j, b + j);
acb_one(tmp + 1 + q);
acb_hypgeom_pfq_direct(tmp, a, p, tmp + 1, q + 1, z, -1, prec);
}
if (regularized && q > 0)
{
acb_t c, t;
acb_init(c);
acb_init(t);
acb_rgamma(c, b, prec);
for (i = 1; i < q; i++)
{
acb_rgamma(t, b + i, prec);
acb_mul(c, c, t, prec);
}
acb_mul(tmp, tmp, c, prec);
acb_clear(c);
acb_clear(t);
}
acb_set(res, tmp);
_acb_vec_clear(tmp, alloc);
}
if (!acb_is_finite(res))
acb_indeterminate(res);
}
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