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
#include <flint/acb_hypgeom.h>Sets res to the rising factorial (x)_n = x(x+1)\cdots(x+n-1); acb_hypgeom_rising allows any complex n and computes \Gamma(x+n)/\Gamma(x).
The forward, bs and rs versions use the forward recurrence, binary splitting and rectangular splitting (with block size m, 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 x, and otherwise uses the forward recurrence for n \le 5 up to 512 bits, binary splitting for n \ge 20 if x has fewer than \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 \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.
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 2026-10-20).
@misc{flint-doc-acb-hypgeom-acb-hypgeom-rising-ui-forward,
author = {{The FLINT team}},
title = {{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)}},
howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
year = {2026},
url = {https://flintlib.org/doc/acb_hypgeom/acb_hypgeom_rising_ui_forward.html},
note = {Generated 2026-10-20}
}