mirror of
https://github.com/vale981/arb
synced 2025-03-05 09:21:38 -05:00
86 lines
1.8 KiB
C
86 lines
1.8 KiB
C
/*
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Copyright (C) 2016 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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/* todo: move this to the acb module? */
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static void
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acb_beta(acb_t res, const acb_t a, const acb_t b, slong prec)
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{
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acb_t t, u;
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acb_init(t);
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acb_init(u);
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acb_gamma(t, a, prec);
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acb_gamma(u, b, prec);
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acb_add(res, a, b, prec);
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acb_rgamma(res, res, prec);
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acb_mul(res, res, t, prec);
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acb_mul(res, res, u, prec);
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acb_clear(t);
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acb_clear(u);
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}
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void acb_hypgeom_beta_lower(acb_t res,
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const acb_t a, const acb_t b, const acb_t z, int regularized, slong prec)
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{
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acb_t t, u;
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if (acb_is_zero(z) && arb_is_positive(acb_realref(a)))
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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 (acb_is_one(z) && arb_is_positive(acb_realref(b)))
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{
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if (regularized)
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acb_one(res);
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else
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acb_beta(res, a, b, prec);
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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_sub_ui(t, b, 1, prec);
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acb_neg(t, t);
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acb_add_ui(u, a, 1, prec);
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if (regularized)
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{
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acb_hypgeom_2f1(t, a, t, u, z, 1, prec);
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acb_add(u, a, b, prec);
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acb_gamma(u, u, prec);
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acb_mul(t, t, u, prec);
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acb_rgamma(u, b, prec);
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acb_mul(t, t, u, prec);
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}
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else
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{
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acb_hypgeom_2f1(t, a, t, u, z, 0, prec);
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acb_div(t, t, a, prec);
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}
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acb_pow(u, z, a, prec);
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acb_mul(t, t, 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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