mirror of
https://github.com/vale981/arb
synced 2025-03-05 09:21:38 -05:00
128 lines
3.1 KiB
C
128 lines
3.1 KiB
C
/*
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Copyright (C) 2016 Arb authors
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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 "arb_poly.h"
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#include "arb_hypgeom.h"
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void
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_arb_hypgeom_gamma_lower_series(arb_ptr g, const arb_t s, arb_srcptr h, slong hlen, int regularized, slong n, slong prec)
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{
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arb_t c;
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hlen = FLINT_MIN(hlen, n);
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if (regularized == 2 && arb_is_int(s) && arb_is_nonpositive(s))
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{
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arb_t ns;
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arb_init(ns);
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arb_neg(ns, s);
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if (g == h)
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{
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arb_ptr t = _arb_vec_init(hlen);
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_arb_vec_set(t, h, hlen);
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_arb_poly_pow_arb_series(g, t, hlen, ns, n, prec);
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_arb_vec_clear(t, hlen);
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}
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else
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{
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_arb_poly_pow_arb_series(g, h, hlen, ns, n, prec);
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}
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arb_clear(ns);
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return;
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}
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arb_init(c);
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arb_hypgeom_gamma_lower(c, s, h, regularized, prec);
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if (hlen == 1)
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{
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_arb_vec_zero(g + 1, n - 1);
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}
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else
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{
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arb_ptr t, u, v;
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arb_ptr w = NULL;
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t = _arb_vec_init(n);
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u = _arb_vec_init(n);
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v = _arb_vec_init(n);
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if (regularized == 2)
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{
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w = _arb_vec_init(n);
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arb_neg(t, s);
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_arb_poly_pow_arb_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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arb_sub_ui(u, s, 1, prec);
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_arb_poly_pow_arb_series(t, h, hlen, u, n, prec);
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_arb_poly_derivative(u, h, hlen, prec);
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_arb_poly_mullow(v, t, n, u, hlen - 1, n, prec);
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_arb_vec_neg(t, h, hlen);
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_arb_poly_exp_series(t, t, hlen, n, prec);
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_arb_poly_mullow(g, v, n, t, n, n, prec);
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_arb_poly_integral(g, g, n, prec);
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if (regularized == 1)
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{
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arb_rgamma(t, s, prec);
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_arb_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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arb_rgamma(t, s, prec);
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_arb_vec_scalar_mul(g, g, n, t, prec);
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_arb_vec_set(u, g, n);
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_arb_poly_mullow(g, u, n, w, n, n, prec);
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_arb_vec_clear(w, n);
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}
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_arb_vec_clear(t, n);
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_arb_vec_clear(u, n);
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_arb_vec_clear(v, n);
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}
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arb_swap(g, c);
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arb_clear(c);
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}
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void
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arb_hypgeom_gamma_lower_series(arb_poly_t g, const arb_t s,
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const arb_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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arb_poly_zero(g);
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return;
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}
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arb_poly_fit_length(g, n);
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if (hlen == 0)
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{
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arb_t t;
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arb_init(t);
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_arb_hypgeom_gamma_lower_series(g->coeffs, s, t, 1, regularized, n, prec);
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arb_clear(t);
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}
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else
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{
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_arb_hypgeom_gamma_lower_series(
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g->coeffs, s, h->coeffs, hlen, regularized, n, prec);
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}
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_arb_poly_set_length(g, n);
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_arb_poly_normalise(g);
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}
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