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/*
Copyright (C) 2016 Fredrik Johansson
This file is part of Arb.
Arb is free software: you can redistribute it and/or modify it under
the terms of the GNU Lesser General Public License (LGPL) as published
by the Free Software Foundation; either version 2.1 of the License, or
(at your option) any later version. See <http://www.gnu.org/licenses/>.
*/
#include "acb_dirichlet.h"
void
acb_dirichlet_zeta_rs_d_coeffs(arb_ptr d, const arb_t sigma, slong k, slong prec)
{
slong j, r, m;
arb_t u;
arb_init(u);
arb_one(u);
arb_submul_ui(u, sigma, 2, prec);
if (k == 0)
{
arb_one(d);
arb_zero(d + 1);
return;
}
for (j = (3 * k) / 2; j >= 0; j--)
{
m = 3 * k - 2 * j;
if (m != 0)
{
arb_mul_2exp_si(d + j, d + j, -1);
if (j >= 1)
arb_addmul(d + j, d + j - 1, u, prec);
arb_div_ui(d + j, d + j, 2 * m, prec);
if (j >= 2)
arb_submul_ui(d + j, d + j - 2, m + 1, prec);
}
}
if (k % 2 == 0)
{
j = (3 * k) / 2;
arb_zero(d + j);
arb_set_ui(u, 2);
for (r = j - 1; r >= 0; r--)
{
if ((j - r) % 2 == 0)
arb_submul(d + j, d + r, u, prec);
else
arb_addmul(d + j, d + r, u, prec);
arb_mul_ui(u, u, 4 * j - 4 * r + 2, prec);
}
}
arb_zero(d + (3 * k) / 2 + 1);
arb_clear(u);
}
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