mirror of
https://github.com/vale981/arb
synced 2025-03-04 17:01:40 -05:00
79 lines
1.8 KiB
C
79 lines
1.8 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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void
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acb_hypgeom_spherical_y(acb_t res, slong n, slong m,
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const acb_t theta, const acb_t phi, slong prec)
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{
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acb_t t, u;
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if (n < 0)
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{
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if (m <= n)
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{
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acb_zero(res);
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return;
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}
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n = -1-n;
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}
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if (m > n || m < -n)
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{
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acb_zero(res);
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return;
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}
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if (n > WORD_MAX / 4)
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{
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acb_indeterminate(res);
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return;
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}
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acb_init(t);
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acb_init(u);
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acb_sin_cos(t, u, theta, prec);
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/* P_n^m(cos(theta)) */
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acb_hypgeom_legendre_p_uiui_rec(u, n, FLINT_ABS(m), u, prec);
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acb_pow_ui(t, t, FLINT_ABS(m), prec);
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acb_mul(t, t, u, prec);
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/* exp(i m phi) */
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acb_mul_onei(u, phi);
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acb_mul_si(u, u, m, prec);
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acb_exp(u, u, prec);
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if (m < 0 && m % 2)
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acb_neg(u, u);
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acb_mul(t, t, u, prec);
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/* sqrt((2n+1)/(4pi) (n-m)!/(n+m)!) */
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arb_fac_ui(acb_realref(u), n - FLINT_ABS(m), prec);
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arb_fac_ui(acb_imagref(u), n + FLINT_ABS(m), prec);
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arb_mul_ui(acb_realref(u), acb_realref(u), 2 * n + 1, prec);
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arb_div(acb_realref(u), acb_realref(u), acb_imagref(u), prec);
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arb_const_pi(acb_imagref(u), prec);
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arb_div(acb_realref(u), acb_realref(u), acb_imagref(u), prec);
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arb_mul_2exp_si(acb_realref(u), acb_realref(u), -2);
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arb_sqrt(acb_realref(u), acb_realref(u), prec);
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acb_mul_arb(t, t, acb_realref(u), prec);
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acb_set(res, t);
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acb_clear(t);
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acb_clear(u);
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}
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