FLINT3.7.0-dev
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arb_hypgeom_gamma_upper

Synopsis#include <flint/arb_hypgeom.h>
void arb_hypgeom_gamma_upper(arb_t res, const arb_t s, const arb_t z, int regularized, slong prec)source

Sets res to the upper incomplete gamma function Γ(s,z)=∫z∞ts−1e−tdt\Gamma(s,z) = \int_z^\infty t^{s-1} e^{-t} dt if regularized is 0, to Q(s,z)=Γ(s,z)/Γ(s)Q(s,z) = \Gamma(s,z)/\Gamma(s) if regularized is 1, and to z−sΓ(s,z)=E1−s(z)z^{-s} \Gamma(s,z) = E_{1-s}(z) if regularized is 2. Wrapper of acb_hypgeom_gamma_upper.

The value is real for z>0z > 0, and for z<0z < 0 only in special cases (such as ss a positive integer). Option 2 is mainly for internal use; arb_hypgeom_expint is the interface for the exponential integral.

Cite this page

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