mirror of
https://github.com/vale981/arb
synced 2025-03-06 09:51:39 -05:00
82 lines
2.1 KiB
C
82 lines
2.1 KiB
C
/*=============================================================================
|
|
|
|
This file is part of ARB.
|
|
|
|
ARB is free software; you can redistribute it and/or modify
|
|
it under the terms of the GNU General Public License as published by
|
|
the Free Software Foundation; either version 2 of the License, or
|
|
(at your option) any later version.
|
|
|
|
ARB is distributed in the hope that it will be useful,
|
|
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
|
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
|
GNU General Public License for more details.
|
|
|
|
You should have received a copy of the GNU General Public License
|
|
along with ARB; if not, write to the Free Software
|
|
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
|
|
|
=============================================================================*/
|
|
/******************************************************************************
|
|
|
|
Copyright (C) 2012 Fredrik Johansson
|
|
|
|
******************************************************************************/
|
|
|
|
#include "acb.h"
|
|
#include "acb_poly.h"
|
|
|
|
void
|
|
acb_hurwitz_zeta(acb_t z, const acb_t s, const acb_t a, long prec)
|
|
{
|
|
_acb_poly_zeta_cpx_series(z, s, a, 0, 1, prec);
|
|
}
|
|
|
|
void
|
|
acb_zeta(acb_t z, const acb_t s, long prec)
|
|
{
|
|
acb_t a;
|
|
acb_init(a);
|
|
acb_one(a);
|
|
|
|
if (arf_sgn(arb_midref(acb_realref(s))) < 0)
|
|
{
|
|
acb_t t, u, v;
|
|
long wp = prec + 6;
|
|
|
|
acb_init(t);
|
|
acb_init(u);
|
|
acb_init(v);
|
|
|
|
acb_sub_ui(t, s, 1, wp);
|
|
|
|
/* 2 * (2pi)^(s-1) */
|
|
arb_const_pi(acb_realref(u), wp);
|
|
acb_mul_2exp_si(u, u, 1);
|
|
acb_pow(u, u, t, wp);
|
|
acb_mul_2exp_si(u, u, 1);
|
|
|
|
/* sin(pi*s/2) */
|
|
acb_mul_2exp_si(v, s, -1);
|
|
acb_sin_pi(v, v, wp);
|
|
acb_mul(u, u, v, wp);
|
|
|
|
/* gamma(1-s) zeta(1-s) */
|
|
acb_neg(t, t);
|
|
acb_gamma(v, t, wp);
|
|
acb_mul(u, u, v, wp);
|
|
acb_hurwitz_zeta(v, t, a, wp);
|
|
acb_mul(z, u, v, prec);
|
|
|
|
acb_clear(t);
|
|
acb_clear(u);
|
|
acb_clear(v);
|
|
}
|
|
else
|
|
{
|
|
acb_hurwitz_zeta(z, s, a, prec);
|
|
}
|
|
|
|
acb_clear(a);
|
|
}
|
|
|