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https://github.com/vale981/arb
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50 lines
1.1 KiB
C
50 lines
1.1 KiB
C
/*
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Copyright (C) 2021 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 "arb_hypgeom.h"
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void
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_arb_hypgeom_gamma_stirling_term_bounds(slong * bound, const mag_t zinv, slong N)
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{
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mag_t b, u;
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slong n;
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mag_init(b);
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mag_init(u);
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/* bound[0] = WORD_MAX; -- should not be used */
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/* first term 1/(12z) */
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mag_set(b, zinv);
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mag_div_ui(b, b, 12);
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bound[1] = MAG_EXP(b);
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/* u = 1/(2 pi z)^2 */
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mag_const_pi_lower(u);
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mag_mul_2exp_si(u, u, 1);
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mag_inv(u, u);
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mag_mul(u, u, zinv);
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mag_mul(u, u, u);
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/* zeta(2n) 2 (2n-2)! / (2pi)^(2n) / z^(2n-1) */
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/* ratio bounded by (2n-2)(2n-3)/(2 pi z)^2 */
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for (n = 2; n < N; n++)
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{
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mag_mul_ui(b, b, (2*n-2) * (2*n-3));
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mag_mul(b, b, u);
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bound[n] = MAG_EXP(b);
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}
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mag_clear(b);
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mag_clear(u);
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}
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