mirror of
https://github.com/vale981/arb
synced 2025-03-05 09:21:38 -05:00
106 lines
2.6 KiB
C
106 lines
2.6 KiB
C
/*
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Copyright (C) 2015 Fredrik Johansson
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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 it under
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the terms of the GNU Lesser General Public License (LGPL) as published
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by the Free Software Foundation; either version 2.1 of the License, or
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(at your option) any later version. See <http://www.gnu.org/licenses/>.
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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_hypgeom_gamma_upper_series(acb_ptr g, const acb_t s, acb_srcptr h, slong hlen, int regularized, slong n, slong 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, regularized, 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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acb_ptr w = NULL;
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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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if (regularized == 2)
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{
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w = _acb_vec_init(n);
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acb_neg(t, s);
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_acb_poly_pow_acb_series(w, h, hlen, t, n, prec);
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}
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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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if (regularized == 1)
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{
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acb_rgamma(t, s, prec);
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_acb_vec_scalar_mul(g, g, n, t, prec);
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}
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else if (regularized == 2)
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{
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_acb_vec_set(u, g, n);
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_acb_poly_mullow(g, u, n, w, n, n, prec);
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_acb_vec_clear(w, n);
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}
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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_hypgeom_gamma_upper_series(acb_poly_t g, const acb_t s,
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const acb_poly_t h, int regularized, slong n, slong prec)
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{
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slong 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_hypgeom_gamma_upper_series(g->coeffs, s, t, 1, regularized, 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_hypgeom_gamma_upper_series(
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g->coeffs, s, h->coeffs, hlen, regularized, 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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