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https://github.com/vale981/arb
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80 lines
1.8 KiB
C
80 lines
1.8 KiB
C
/*
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Copyright (C) 2016 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_hypgeom.h"
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void
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_acb_hypgeom_ei_series(acb_ptr g, acb_srcptr h, slong hlen, slong len, slong prec)
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{
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acb_t c;
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if (acb_contains_zero(h))
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{
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_acb_vec_indeterminate(g, len);
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return;
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}
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acb_init(c);
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acb_hypgeom_ei(c, h, prec);
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hlen = FLINT_MIN(hlen, len);
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if (hlen == 1)
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{
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_acb_vec_zero(g + 1, len - 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(len);
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u = _acb_vec_init(len);
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v = _acb_vec_init(len);
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/* Ei(h(x)) = integral([h'(x) / h(x)] exp(h(x)) */
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_acb_poly_exp_series(t, h, hlen, len - 1, prec);
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_acb_poly_derivative(u, h, hlen, prec);
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_acb_poly_mullow(v, t, len - 1, u, len - 1, len - 1, prec);
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_acb_poly_div_series(u, v, len - 1, h, hlen, len - 1, prec);
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_acb_poly_integral(g, u, len, prec);
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_acb_vec_clear(t, len);
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_acb_vec_clear(u, len);
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_acb_vec_clear(v, len);
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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_ei_series(acb_poly_t g, const acb_poly_t h, slong len, slong prec)
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{
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slong hlen = h->length;
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if (len == 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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if (hlen == 0)
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{
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acb_poly_inv_series(g, h, len, prec);
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return;
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}
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acb_poly_fit_length(g, len);
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_acb_hypgeom_ei_series(g->coeffs, h->coeffs, hlen, len, prec);
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_acb_poly_set_length(g, len);
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_acb_poly_normalise(g);
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}
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