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/*
Copyright (C) 2012 Fredrik Johansson
This file is part of FLINT.
FLINT 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 3 of the License, or
(at your option) any later version. See <https://www.gnu.org/licenses/>.
*/
#include "fmpq.h"
#include "arb.h"
#include "bernoulli.h"
void
arb_zeta_ui_bernoulli(arb_t x, ulong n, slong prec)
{
fmpq_t b;
arb_t t, f;
slong wp;
if (n % 2)
flint_throw(FLINT_ERROR, "(%s)\n", __func__);
wp = prec + FLINT_BIT_COUNT(n) + 2;
fmpq_init(b);
arb_init(t);
arb_init(f);
bernoulli_fmpq_ui(b, n);
arb_set_fmpq(x, b, wp);
arb_const_pi(t, wp);
arb_mul_2exp_si(t, t, 1);
arb_pow_ui(t, t, n, wp);
arb_fac_ui(f, n, wp);
arb_div(t, t, f, wp);
arb_mul(x, x, t, wp);
arb_abs(x, x);
arb_mul_2exp_si(x, x, -1);
arb_clear(t);
arb_clear(f);
fmpq_clear(b);
}