mirror of
https://github.com/vale981/arb
synced 2025-03-06 09:51:39 -05:00
99 lines
2.7 KiB
C
99 lines
2.7 KiB
C
/*=============================================================================
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This file is part of ARB.
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ARB is free software; you can redistribute it and/or modify
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation; either version 2 of the License, or
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(at your option) any later version.
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ARB is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with ARB; if not, write to the Free Software
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Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
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=============================================================================*/
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/******************************************************************************
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Copyright (C) 2015 Fredrik Johansson
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******************************************************************************/
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#include "acb_poly.h"
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#include "acb_hypgeom.h"
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void
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_acb_poly_gamma_upper_series(acb_ptr g, const acb_t s, acb_srcptr h, long hlen, long n, long prec)
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{
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acb_t c;
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acb_init(c);
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acb_hypgeom_gamma_upper(c, s, h, 0, prec);
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hlen = FLINT_MIN(hlen, n);
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if (hlen == 1)
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{
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_acb_vec_zero(g + 1, n - 1);
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}
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else
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{
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acb_ptr t, u, v;
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t = _acb_vec_init(n);
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u = _acb_vec_init(n);
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v = _acb_vec_init(n);
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/* Gamma(s, h(x)) = -integral(h'(x) h(x)^(s-1) exp(-h(x)) */
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acb_sub_ui(u, s, 1, prec);
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_acb_poly_pow_acb_series(t, h, hlen, u, n, prec);
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_acb_poly_derivative(u, h, hlen, prec);
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_acb_poly_mullow(v, t, n, u, hlen - 1, n, prec);
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_acb_vec_neg(t, h, hlen);
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_acb_poly_exp_series(t, t, hlen, n, prec);
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_acb_poly_mullow(g, v, n, t, n, n, prec);
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_acb_poly_integral(g, g, n, prec);
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_acb_vec_neg(g, g, n);
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_acb_vec_clear(t, n);
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_acb_vec_clear(u, n);
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_acb_vec_clear(v, n);
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}
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acb_swap(g, c);
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acb_clear(c);
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}
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void
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acb_poly_gamma_upper_series(acb_poly_t g, const acb_t s, const acb_poly_t h, long n, long prec)
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{
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long hlen = h->length;
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if (n == 0)
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{
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acb_poly_zero(g);
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return;
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}
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acb_poly_fit_length(g, n);
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if (hlen == 0)
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{
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acb_t t;
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acb_init(t);
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_acb_poly_gamma_upper_series(g->coeffs, s, t, 1, n, prec);
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acb_clear(t);
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}
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else
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{
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_acb_poly_gamma_upper_series(g->coeffs, s, h->coeffs, hlen, n, prec);
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}
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_acb_poly_set_length(g, n);
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_acb_poly_normalise(g);
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}
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