mirror of
https://github.com/vale981/arb
synced 2025-03-05 09:21:38 -05:00
104 lines
2.5 KiB
C
104 lines
2.5 KiB
C
/*
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Copyright (C) 2015 Fredrik Johansson
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This file is part of Arb.
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Arb is free software: you can redistribute it and/or modify it under
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the terms of the GNU Lesser General Public License (LGPL) as published
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by the Free Software Foundation; either version 2.1 of the License, or
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(at your option) any later version. See <http://www.gnu.org/licenses/>.
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*/
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#include "acb_hypgeom.h"
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static void
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phase(acb_t res, const arb_t re, const arb_t im)
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{
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if (arb_is_nonnegative(re) || arb_is_negative(im))
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{
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acb_one(res);
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}
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else if (arb_is_negative(re) && arb_is_nonnegative(im))
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{
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acb_set_si(res, -3);
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}
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else
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{
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arb_zero(acb_imagref(res));
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/* -1 +/- 2 */
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arf_set_si(arb_midref(acb_realref(res)), -1);
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mag_one(arb_radref(acb_realref(res)));
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mag_mul_2exp_si(arb_radref(acb_realref(res)), arb_radref(acb_realref(res)), 1);
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}
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}
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void
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acb_hypgeom_bessel_jy(acb_t res1, acb_t res2, const acb_t nu, const acb_t z, slong prec)
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{
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acb_t jnu, t, u, v;
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/* both j and y are zero at -inf and +inf when nu is finite */
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if (acb_is_finite(nu) && !acb_is_finite(z) &&
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acb_is_real(z) && !acb_contains_zero(z))
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{
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if (res1 != NULL) acb_zero(res1);
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acb_zero(res2);
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return;
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}
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acb_init(jnu);
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acb_init(t);
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acb_init(u);
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acb_init(v);
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acb_hypgeom_bessel_j(jnu, nu, z, prec);
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if (acb_is_int(nu))
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{
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int is_real = acb_is_real(nu) && acb_is_real(z)
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&& arb_is_positive(acb_realref(z));
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acb_mul_onei(t, z);
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acb_hypgeom_bessel_k(t, nu, t, prec);
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acb_onei(u);
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acb_pow(u, u, nu, prec);
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acb_mul(t, t, u, prec);
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acb_const_pi(u, prec);
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acb_div(t, t, u, prec);
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acb_mul_2exp_si(t, t, 1);
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acb_neg(t, t);
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phase(v, acb_realref(z), acb_imagref(z));
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acb_mul(u, jnu, v, prec);
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acb_mul_onei(u, u);
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acb_sub(res2, t, u, prec);
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if (is_real)
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arb_zero(acb_imagref(res2));
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}
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else
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{
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acb_sin_cos_pi(t, u, nu, prec);
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acb_mul(v, jnu, u, prec);
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acb_neg(u, nu);
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acb_hypgeom_bessel_j(u, u, z, prec);
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acb_sub(v, v, u, prec);
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acb_div(res2, v, t, prec);
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}
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if (res1 != NULL)
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acb_set(res1, jnu);
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acb_clear(jnu);
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acb_clear(t);
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acb_clear(u);
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acb_clear(v);
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}
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void
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acb_hypgeom_bessel_y(acb_t res, const acb_t nu, const acb_t z, slong prec)
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{
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acb_hypgeom_bessel_jy(NULL, res, nu, z, prec);
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}
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