mirror of
https://github.com/vale981/arb
synced 2025-03-06 01:41:39 -05:00
130 lines
3.2 KiB
C
130 lines
3.2 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) 2014 Fredrik Johansson
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******************************************************************************/
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#include "acb_hypgeom.h"
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void
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acb_hypgeom_pfq_sum_rs(acb_t res, acb_t term, acb_srcptr a, long p,
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acb_srcptr b, long q, const acb_t z, long n, long prec)
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{
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acb_ptr zpow;
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acb_t s, t, u;
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long i, j, k, m;
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mag_t B, C;
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if (n == 0)
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{
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acb_zero(res);
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acb_one(term);
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return;
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}
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if (n < 0)
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abort();
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m = n_sqrt(n);
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m = FLINT_MIN(m, 150);
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mag_init(B);
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mag_init(C);
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acb_init(s);
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acb_init(t);
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acb_init(u);
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zpow = _acb_vec_init(m + 1);
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_acb_vec_set_powers(zpow, z, m + 1, prec);
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mag_one(B);
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for (k = n; k >= 0; k--)
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{
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j = k % m;
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if (k < n)
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acb_add(s, s, zpow + j, prec);
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if (k > 0)
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{
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if (p > 0)
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{
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acb_add_ui(u, a, k - 1, prec);
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for (i = 1; i < p; i++)
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{
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acb_add_ui(t, a + i, k - 1, prec);
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acb_mul(u, u, t, prec);
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}
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if (k < n)
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acb_mul(s, s, u, prec);
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acb_get_mag(C, u);
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mag_mul(B, B, C);
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}
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if (q > 0)
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{
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acb_add_ui(u, b, k - 1, prec);
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for (i = 1; i < q; i++)
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{
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acb_add_ui(t, b + i, k - 1, prec);
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acb_mul(u, u, t, prec);
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}
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if (k < n)
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acb_div(s, s, u, prec);
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acb_get_mag_lower(C, u);
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mag_div(B, B, C);
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}
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if (j == 0 && k < n)
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{
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acb_mul(s, s, zpow + m, prec);
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}
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}
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}
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acb_get_mag(C, z);
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mag_pow_ui(C, C, n);
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mag_mul(B, B, C);
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acb_zero(term);
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if (_acb_vec_is_real(a, p) && _acb_vec_is_real(b, q) && acb_is_real(z))
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arb_add_error_mag(acb_realref(term), B);
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else
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acb_add_error_mag(term, B);
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acb_set(res, s);
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mag_clear(B);
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mag_clear(C);
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acb_clear(s);
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acb_clear(t);
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acb_clear(u);
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_acb_vec_clear(zpow, m + 1);
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}
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