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/*
Copyright (C) 2013 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 "arb_poly.h"
void
_arb_poly_asin_series(arb_ptr g, arb_srcptr h, slong hlen, slong n, slong prec)
{
arb_t c;
arb_init(c);
arb_asin(c, h, prec);
hlen = FLINT_MIN(hlen, n);
if (hlen == 1)
{
_arb_vec_zero(g + 1, n - 1);
}
else
{
arb_ptr t, u;
slong ulen;
t = _arb_vec_init(n);
u = _arb_vec_init(n);
/* asin(h(x)) = integral(h'(x)/sqrt(1-h(x)^2)) */
ulen = FLINT_MIN(n, 2 * hlen - 1);
_arb_poly_mullow(u, h, hlen, h, hlen, ulen, prec);
arb_sub_ui(u, u, 1, prec);
_arb_vec_neg(u, u, ulen);
_arb_poly_rsqrt_series(t, u, ulen, n, prec);
_arb_poly_derivative(u, h, hlen, prec);
_arb_poly_mullow(g, t, n, u, hlen - 1, n, prec);
_arb_poly_integral(g, g, n, prec);
_arb_vec_clear(t, n);
_arb_vec_clear(u, n);
}
arb_swap(g, c);
arb_clear(c);
}
void
arb_poly_asin_series(arb_poly_t g, const arb_poly_t h, slong n, slong prec)
{
slong hlen = h->length;
if (hlen == 0 || n == 0)
{
arb_poly_zero(g);
return;
}
arb_poly_fit_length(g, n);
_arb_poly_asin_series(g->coeffs, h->coeffs, hlen, n, prec);
_arb_poly_set_length(g, n);
_arb_poly_normalise(g);
}
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