FLINT3.7.0-dev
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ca_gamma

Synopsis#include <flint/ca.h>
void ca_gamma(ca_t res, const ca_t x, ca_ctx_t ctx)source

Sets res to Γ(x)\Gamma(x). Integers give factorials (or ∞~\tilde \infty at the poles 0,−1,−2,…0, -1, -2, \ldots), half-integers give rational multiples of π\sqrt{\pi}, and otherwise the result is an element of a field containing Γ(x)\Gamma(x); the relation Γ(x+n)=x(x+1)⋯(x+n−1)Γ(x)\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: Γ(+∞)=+∞\Gamma(+\infty) = +\infty; Γ(−∞)\Gamma(-\infty), Γ(∞~)\Gamma(\tilde \infty) and Γ(Undefined)\Gamma(\text{Undefined}) are Undefined; Γ(±i∞)=0\Gamma(\pm i \infty) = 0; and the result is Unknown for Unknown and for other signed infinities.

Cite this page

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 2026-11-02).