mirror of
https://github.com/vale981/arb
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74 lines
1.6 KiB
C
74 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.h"
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#include "acb_poly.h"
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void
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acb_polygamma(acb_t res, const acb_t s, const acb_t z, slong prec)
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{
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if (acb_is_zero(s))
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{
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acb_digamma(res, z, prec);
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}
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else if (acb_is_int(s) && arb_is_positive(acb_realref(s)))
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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_add_ui(t, s, 1, prec);
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acb_gamma(u, t, prec);
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acb_hurwitz_zeta(t, t, z, prec);
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if (acb_is_int_2exp_si(s, 1))
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acb_neg(t, t);
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acb_mul(res, t, u, prec);
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acb_clear(t);
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acb_clear(u);
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}
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else
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{
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acb_t t, u;
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acb_struct v[2];
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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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acb_init(v + 1);
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/* u = psi(-s) + gamma */
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acb_neg(t, s);
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acb_digamma(u, t, prec);
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arb_const_euler(acb_realref(v), prec);
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arb_add(acb_realref(u), acb_realref(u), acb_realref(v), prec);
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acb_add_ui(t, s, 1, prec);
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_acb_poly_zeta_cpx_series(v, t, z, 0, 2, prec);
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acb_addmul(v + 1, v, u, prec);
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acb_neg(t, s);
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acb_rgamma(u, t, prec);
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acb_mul(res, v + 1, u, prec);
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acb_clear(v);
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acb_clear(v + 1);
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acb_clear(t);
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acb_clear(u);
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}
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}
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