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/*
Copyright (C) 2021 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 "arb.h"
#include "arb_hypgeom.h"
void
arb_hypgeom_bessel_i_integration(arb_t res, const arb_t nu, const arb_t z, int scaled, slong prec)
{
arb_t t, a, b, w;
arb_init(t);
arb_init(a);
arb_init(b);
arb_init(w);
arb_one(a);
arb_mul_2exp_si(a, a, -1);
arb_add(a, a, nu, prec);
arb_mul_2exp_si(b, nu, 1);
arb_add_ui(b, b, 1, prec);
arb_mul_2exp_si(w, z, 1);
arb_hypgeom_1f1_integration(t, a, b, w, 0, prec);
if (arb_is_finite(t))
{
if (!scaled)
{
arb_neg(a, z);
arb_exp(a, a, prec);
arb_mul(t, t, a, prec);
}
else
{
arb_neg(a, z);
arb_mul_2exp_si(a, a, 1);
arb_exp(a, a, prec);
arb_mul(t, t, a, prec);
}
arb_mul_2exp_si(w, z, -1);
arb_pow(w, w, nu, prec);
arb_mul(t, t, w, prec);
arb_add_ui(w, nu, 1, prec);
arb_rgamma(w, w, prec);
arb_mul(res, t, w, prec);
}
else
{
arb_indeterminate(res);
}
arb_clear(t);
arb_clear(a);
arb_clear(b);
arb_clear(w);
}