FLINT3.7.0-dev
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acb_hypgeom_rising_ui_forward, acb_hypgeom_rising_ui_bs, acb_hypgeom_rising_ui_rs, acb_hypgeom_rising_ui_rec, acb_hypgeom_rising_ui, acb_hypgeom_rising

Synopsis#include <flint/acb_hypgeom.h>
void acb_hypgeom_rising_ui_forward(acb_t res, const acb_t x, ulong n, slong prec)source
void acb_hypgeom_rising_ui_bs(acb_t res, const acb_t x, ulong n, slong prec)source
void acb_hypgeom_rising_ui_rs(acb_t res, const acb_t x, ulong n, ulong m, slong prec)source
void acb_hypgeom_rising_ui_rec(acb_t res, const acb_t x, ulong n, slong prec)source
void acb_hypgeom_rising_ui(acb_t res, const acb_t x, ulong n, slong prec)source
void acb_hypgeom_rising(acb_t res, const acb_t x, const acb_t n, slong prec)source

Sets res to the rising factorial (x)n=x(x+1)⋯(x+n−1)(x)_n = x(x+1)\cdots(x+n-1); acb_hypgeom_rising allows any complex nn and computes Γ(x+n)/Γ(x)\Gamma(x+n)/\Gamma(x).

The forward, bs and rs versions use the forward recurrence, binary splitting and rectangular splitting (with block size mm, or 0 to choose it), as for the real functions arb_hypgeom_rising_ui_forward and its relatives. acb_hypgeom_rising_ui_rec calls the real version for real xx, and otherwise uses the forward recurrence for n≤5n \le 5 up to 512 bits, binary splitting for n≥20n \ge 20 if xx has fewer than prec/8\mathit{prec}/8 bits, and rectangular splitting otherwise; it never calls the gamma function. acb_hypgeom_rising_ui and acb_hypgeom_rising use it for integers 0≤n<max⁡(prec,100)0 \le n < \max(\mathit{prec}, 100) and the gamma function otherwise. These are the functions behind acb_rising_ui and acb_rising. See Rising factorials.

Cite this page

The FLINT team, “acb_hypgeom_rising_ui_forward, acb_hypgeom_rising_ui_bs, acb_hypgeom_rising_ui_rs, acb_hypgeom_rising_ui_rec, acb_hypgeom_rising_ui, acb_hypgeom_rising (acb_hypgeom.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/acb_hypgeom/acb_hypgeom_rising_ui_forward.html (generated 2026-11-02).