mirror of
https://github.com/vale981/arb
synced 2025-03-04 17:01:40 -05:00
82 lines
1.8 KiB
C
82 lines
1.8 KiB
C
/*
|
|
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_li_series(acb_ptr g, acb_srcptr h, slong hlen, int offset, slong len, slong prec)
|
|
{
|
|
acb_t c;
|
|
|
|
if (acb_contains_zero(h))
|
|
{
|
|
_acb_vec_indeterminate(g, len);
|
|
return;
|
|
}
|
|
|
|
acb_init(c);
|
|
acb_hypgeom_li(c, h, offset, prec);
|
|
|
|
hlen = FLINT_MIN(hlen, len);
|
|
|
|
if (hlen == 1)
|
|
{
|
|
_acb_vec_zero(g + 1, len - 1);
|
|
}
|
|
else if (len == 2)
|
|
{
|
|
acb_log(g, h, prec);
|
|
acb_div(g + 1, h + 1, g, prec);
|
|
}
|
|
else
|
|
{
|
|
acb_ptr t, u;
|
|
|
|
t = _acb_vec_init(len);
|
|
u = _acb_vec_init(hlen);
|
|
|
|
/* li(h(x)) = integral(h'(x) / log(h(x))) */
|
|
_acb_poly_log_series(t, h, hlen, len - 1, prec);
|
|
_acb_poly_derivative(u, h, hlen, prec);
|
|
_acb_poly_div_series(g, u, hlen - 1, t, len - 1, len - 1, prec);
|
|
_acb_poly_integral(g, g, len, prec);
|
|
|
|
_acb_vec_clear(t, len);
|
|
_acb_vec_clear(u, hlen);
|
|
}
|
|
|
|
acb_swap(g, c);
|
|
acb_clear(c);
|
|
}
|
|
|
|
void
|
|
acb_hypgeom_li_series(acb_poly_t g, const acb_poly_t h, int offset, 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_li_series(g->coeffs, h->coeffs, hlen, offset, len, prec);
|
|
_acb_poly_set_length(g, len);
|
|
_acb_poly_normalise(g);
|
|
}
|
|
|