FLINT3.7.0-dev
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acb_barnes_g, acb_log_barnes_g

Synopsis#include <flint/acb.h>
void acb_barnes_g(acb_t res, const acb_t z, slong prec)source
void acb_log_barnes_g(acb_t res, const acb_t z, slong prec)source

Set res to the Barnes G-function, respectively its logarithm, which has its branch cut on the negative real axis and satisfies log⁡G(z+1)=log⁡Γ(z)+log⁡G(z)\log G(z + 1) = \log \Gamma(z) + \log G(z) for all zz.

Small integers use the recurrence G(z+1)=Γ(z)G(z)G(z + 1) = \Gamma(z) G(z) with G(1)=1G(1) = 1. Otherwise log⁡G(z)=(z−1)log⁡Γ(z)−ζ′(−1,z)+ζ′(−1)\log G(z) = (z - 1) \log \Gamma(z) - \zeta'(-1, z) + \zeta'(-1).

Cite this page

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