FLINT3.7.0-dev
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gr_gamma_upper, gr_gamma_lower

Synopsis#include <flint/gr_special.h>
int gr_gamma_upper(gr_ptr res, gr_srcptr x, gr_srcptr y, int regularized, gr_ctx_t ctx)source
int gr_gamma_lower(gr_ptr res, gr_srcptr x, gr_srcptr y, int regularized, gr_ctx_t ctx)source

Set res to the incomplete gamma functions with parameter s=xs = x and argument z=yz = y: if regularized is 0, the upper function Γ(s,z)=∫z∞ts−1e−t dt\Gamma(s, z) = \int_z^\infty t^{s-1} e^{-t} \, dt and the lower function γ(s,z)=∫0zts−1e−t dt\gamma(s, z) = \int_0^z t^{s-1} e^{-t} \, dt; if 1, the regularized versions Q(s,z)=Γ(s,z)/Γ(s)Q(s, z) = \Gamma(s,z)/\Gamma(s) and P(s,z)=γ(s,z)/Γ(s)P(s,z) = \gamma(s,z)/\Gamma(s); if 2, z−sΓ(s,z)z^{-s} \Gamma(s, z) and γ∗(s,z)=z−sP(s,z)\gamma^*(s, z) = z^{-s} P(s, z), as for acb_hypgeom_gamma_upper and acb_hypgeom_gamma_lower.

Cite this page

The FLINT team, “gr_gamma_upper, gr_gamma_lower (gr_special.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/gr_special/gr_gamma_upper.html (generated 2026-11-02).