mirror of
https://github.com/vale981/arb
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75 lines
1.6 KiB
C
75 lines
1.6 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_legendre_p_uiui_rec(acb_t res, ulong n, ulong m, const acb_t z, slong prec)
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{
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acb_t t, u, v;
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slong k;
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if (!acb_is_finite(z))
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{
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acb_indeterminate(res);
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return;
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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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if ((n - m) / 4 > prec)
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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_init(v);
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/* t = p(m,m) = (-1)^m (2m-1)!! */
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if (m == 0)
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arb_one(acb_realref(t));
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else
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arb_doublefac_ui(acb_realref(t), 2 * m - 1, prec);
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if (m % 2)
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arb_neg(acb_realref(t), acb_realref(t));
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if (n > m)
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{
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/* t = p(m+1,m) = z(2m+1)p(m,m), u = p(m,m) */
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acb_mul_ui(u, t, 2 * m + 1, prec);
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acb_mul(u, u, z, prec);
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acb_swap(t, u);
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for (k = m + 2; k <= n; k++)
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{
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/* t, u = ((2*k-1)*z*t - (k+m-1)*u) / (k-m), t */
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acb_mul(v, t, z, prec);
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acb_mul_ui(v, v, 2 * k - 1, prec);
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acb_submul_ui(v, u, k + m - 1, prec);
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acb_div_ui(u, v, k - m, prec);
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acb_swap(t, u);
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}
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}
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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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acb_clear(v);
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}
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