FLINT3.7.0-dev
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_acb_mzeta_gamma_upper_scaled

Synopsis#include <flint/acb_mzeta.h>
void _acb_mzeta_gamma_upper_scaled(acb_t res, const acb_t a, const arb_t t, const acb_t ga, slong prec)source

Sets res to t−aΓ(a,t)=∫1∞ua−1e−tu dut^{-a} \Gamma(a, t) = \int_1^\infty u^{a-1} e^{-tu}\, du for real t>0t > 0 to a relative accuracy of about prec bits; ga is Γ(a)\Gamma(a) (at a sufficient precision) or NULL.

The method (asymptotic series, convergent series with the working precision raised to cover its cancellation, or an expression in E1E_1 for nonpositive integers aa) and the working precision are chosen here for the lattice sums, which need many values with one aa. A ball tt is evaluated at its midpoint, with the radius propagated through a bound for the derivative; see The scaled incomplete gamma function.

Cite this page

The FLINT team, “_acb_mzeta_gamma_upper_scaled (acb_mzeta.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/acb_mzeta/_acb_mzeta_gamma_upper_scaled.html (generated 2026-11-07).