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/*
Copyright (C) 2016 Pascal Molin
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"
/* sum a_k x^(k^2), assume a[0] = 0 */
void
acb_dirichlet_qseries_arb(acb_t res, acb_srcptr a, const arb_t x, slong len, slong prec)
{
slong k;
arb_t xk2, dx, x2;
arb_init(xk2);
arb_init(dx);
arb_init(x2);
arb_set(dx, x);
arb_set(xk2, dx);
arb_mul(x2, dx, dx, prec);
acb_mul_arb(res, a + 1, xk2, prec);
/* TODO: reduce prec */
for (k = 2; k < len; k++)
{
arb_mul(dx, dx, x2, prec);
arb_mul(xk2, xk2, dx, prec);
acb_addmul_arb(res, a + k, xk2, prec);
}
arb_clear(xk2);
arb_clear(x2);
arb_clear(dx);
}
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