mirror of
https://github.com/vale981/arb
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59 lines
1.7 KiB
C
59 lines
1.7 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_hypgeom.h"
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void
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acb_hypgeom_2f1_corner(acb_t res, const acb_t a, const acb_t b,
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const acb_t c, const acb_t z, int regularized, slong prec)
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{
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acb_t aa, bb, cc, z1, z2, f1, f2;
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int upper;
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acb_init(aa); acb_init(bb); acb_init(cc);
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acb_init(z1); acb_init(z2); acb_init(f1); acb_init(f2);
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acb_add_ui(aa, a, 1, prec);
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acb_add_ui(bb, b, 1, prec);
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acb_add_ui(cc, c, 1, prec);
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upper = arb_is_positive(acb_imagref(z));
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/* 0 -> 0.5 +/- 0.5i -> 0.5 +/- 0.75i -> z */
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#if 0
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acb_set_d_d(z1, 0.5, upper ? 0.5 : -0.5);
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acb_set_d_d(z2, 0.5, upper ? 0.75 : -0.75);
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#else
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acb_set_d_d(z1, 0.375, upper ? 0.625 : -0.625);
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acb_set_d_d(z2, 0.5, upper ? 0.8125 : -0.8125);
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#endif
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acb_hypgeom_2f1_direct(f1, a, b, c, z1, regularized, prec);
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acb_hypgeom_2f1_direct(f2, aa, bb, cc, z1, regularized, prec);
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acb_mul(f2, f2, a, prec);
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acb_mul(f2, f2, b, prec);
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if (!regularized)
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acb_div(f2, f2, c, prec);
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acb_hypgeom_2f1_continuation(f1, f2, a, b, c, z1, z2, f1, f2, prec);
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acb_set(z1, z2);
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acb_set(z2, z);
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acb_hypgeom_2f1_continuation(f1, f2, a, b, c, z1, z2, f1, f2, prec);
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acb_set(res, f1);
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acb_clear(aa); acb_clear(bb); acb_clear(cc);
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acb_clear(z1); acb_clear(z2); acb_clear(f1); acb_clear(f2);
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}
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