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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 "arb_hypgeom.h"
#include "acb_hypgeom.h"
void
acb_hypgeom_si_asymp(acb_t res, const acb_t z, slong prec)
{
acb_t t, u, w, v, one;
acb_init(t);
acb_init(u);
acb_init(w);
acb_init(v);
acb_init(one);
acb_one(one);
acb_mul_onei(w, z);
/* u = U(1,1,iz) */
acb_hypgeom_u_asymp(u, one, one, w, -1, prec);
/* v = e^(-iz) */
acb_neg(v, w);
acb_exp(v, v, prec);
acb_mul(t, u, v, prec);
if (acb_is_real(z))
{
arb_div(acb_realref(t), acb_realref(t), acb_realref(z), prec);
arb_zero(acb_imagref(t));
acb_neg(t, t);
}
else
{
/* u = U(1,1,-iz) */
acb_neg(w, w);
acb_hypgeom_u_asymp(u, one, one, w, -1, prec);
acb_inv(v, v, prec);
acb_addmul(t, u, v, prec);
acb_div(t, t, z, prec);
acb_mul_2exp_si(t, t, -1);
acb_neg(t, t);
}
if (arb_is_zero(acb_realref(z)))
{
/* the function is imaginary */
arb_zero(acb_realref(t));
}
else if (arb_is_positive(acb_realref(z)))
{
acb_const_pi(u, prec);
acb_mul_2exp_si(u, u, -1);
arb_add(acb_realref(t), acb_realref(t), acb_realref(u), prec);
}
else if (arb_is_negative(acb_realref(z)))
{
acb_const_pi(u, prec);
acb_mul_2exp_si(u, u, -1);
arb_sub(acb_realref(t), acb_realref(t), acb_realref(u), prec);
}
else
{
/* add [-pi,pi]/2 */
acb_const_pi(u, prec);
acb_mul_2exp_si(u, u, -1);
arb_add_error(acb_imagref(t), acb_realref(u));
}
acb_swap(res, t);
acb_clear(t);
acb_clear(u);
acb_clear(w);
acb_clear(v);
acb_clear(one);
}
void
acb_hypgeom_si_1f2(acb_t res, const acb_t z, slong prec)
{
acb_t a, t;
acb_struct b[3];
acb_init(a);
acb_init(b);
acb_init(b + 1);
acb_init(b + 2);
acb_init(t);
acb_one(a);
acb_mul_2exp_si(a, a, -1);
acb_set_ui(b, 3);
acb_mul_2exp_si(b, b, -1);
acb_set(b + 1, b);
acb_one(b + 2);
acb_mul(t, z, z, prec);
acb_mul_2exp_si(t, t, -2);
acb_neg(t, t);
acb_hypgeom_pfq_direct(t, a, 1, b, 3, t, -1, prec);
acb_mul(t, t, z, prec);
acb_swap(res, t);
acb_clear(a);
acb_clear(b);
acb_clear(b + 1);
acb_clear(b + 2);
acb_clear(t);
}
void
acb_hypgeom_si(acb_t res, const acb_t z, slong prec)
{
if (acb_is_real(z) && arb_is_finite(acb_realref(z)))
{
arb_hypgeom_si(acb_realref(res), acb_realref(z), prec);
arb_zero(acb_imagref(res));
return;
}
if (acb_hypgeom_u_use_asymp(z, prec))
acb_hypgeom_si_asymp(res, z, prec);
else
acb_hypgeom_si_1f2(res, z, prec);
}
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