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https://github.com/vale981/arb
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50 lines
1.3 KiB
C
50 lines
1.3 KiB
C
/*
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Copyright (C) 2017 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_dirichlet.h"
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void
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acb_dirichlet_hurwitz(acb_t res, const acb_t s, const acb_t a, slong prec)
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{
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if (acb_is_one(a))
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{
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acb_dirichlet_zeta(res, s, prec);
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return;
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}
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if (acb_is_zero(s))
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{
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acb_mul_2exp_si(res, a, 1);
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acb_sub_ui(res, res, 1, prec);
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acb_neg(res, res);
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acb_mul_2exp_si(res, res, -1);
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return;
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}
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if (acb_is_int(s) && arf_sgn(arb_midref(acb_realref(s))) < 0 &&
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arf_cmpabs_ui(arb_midref(acb_realref(s)), prec / 2) < 0)
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{
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slong n = arf_get_si(arb_midref(acb_realref(s)), ARF_RND_FLOOR);
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acb_bernoulli_poly_ui(res, 1 - n, a, prec);
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acb_div_si(res, res, n - 1, prec);
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return;
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}
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if (arb_contains_zero(acb_imagref(s)) && arb_contains_si(acb_realref(s), 1))
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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_poly_zeta_cpx_series(res, s, a, 0, 1, prec);
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}
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