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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_hypgeom.h"
void
_acb_hypgeom_ci_series(acb_ptr g, acb_srcptr h, slong hlen, slong len, slong prec)
{
acb_t c;
if (acb_contains_zero(h))
{
_acb_vec_indeterminate(g, len);
return;
}
acb_init(c);
acb_hypgeom_ci(c, h, prec);
hlen = FLINT_MIN(hlen, len);
if (hlen == 1)
{
_acb_vec_zero(g + 1, len - 1);
}
else
{
acb_ptr t, u, v;
t = _acb_vec_init(len);
u = _acb_vec_init(len);
v = _acb_vec_init(len);
/* Ci(h(x)) = integral([h'(x) / h(x)] cos(h(x)) */
_acb_poly_cos_series(t, h, hlen, len - 1, prec);
_acb_poly_derivative(u, h, hlen, prec);
_acb_poly_mullow(v, t, len - 1, u, len - 1, len - 1, prec);
_acb_poly_div_series(u, v, len - 1, h, hlen, len - 1, prec);
_acb_poly_integral(g, u, len, prec);
_acb_vec_clear(t, len);
_acb_vec_clear(u, len);
_acb_vec_clear(v, len);
}
acb_swap(g, c);
acb_clear(c);
}
void
acb_hypgeom_ci_series(acb_poly_t g, const acb_poly_t h, slong len, slong prec)
{
slong hlen = h->length;
if (len == 0)
{
acb_poly_zero(g);
return;
}
if (hlen == 0)
{
acb_poly_inv_series(g, h, len, prec);
return;
}
acb_poly_fit_length(g, len);
_acb_hypgeom_ci_series(g->coeffs, h->coeffs, hlen, len, prec);
_acb_poly_set_length(g, len);
_acb_poly_normalise(g);
}
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