ca_gamma
#include <flint/ca.h>Sets res to \Gamma(x). Integers give factorials (or \tilde \infty at the poles 0, -1, -2, \ldots), half-integers give rational multiples of \sqrt{\pi}, and otherwise the result is an element of a field containing \Gamma(x); the relation \Gamma(x + n) = x (x+1) \cdots (x+n-1) \Gamma(x) between generators that differ by integers is added to the ideal of relations.
For special values: \Gamma(+\infty) = +\infty; \Gamma(-\infty), \Gamma(\tilde \infty) and \Gamma(\text{Undefined}) are Undefined; \Gamma(\pm i \infty) = 0; and the result is Unknown for Unknown and for other signed infinities.
The FLINT team, “ca_gamma (ca.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/ca/ca_gamma.html (generated 2026-10-20).
@misc{flint-doc-ca-ca-gamma,
author = {{The FLINT team}},
title = {{ca\_gamma (ca.h)}},
howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
year = {2026},
url = {https://flintlib.org/doc/ca/ca_gamma.html},
note = {Generated 2026-10-20}
}