FLINT3.7.0-dev
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_arb_hypgeom_gamma_fmpq_jet

Synopsis#include <flint/arb_hypgeom.h>
void _arb_hypgeom_gamma_fmpq_jet(arb_ptr res, const fmpq_t a, slong len, slong prec)source

Sets res to the jet of Γ(a+ε)\Gamma(a + \varepsilon) for rational aa which is not a nonpositive integer, computed as γ(a+ε,Z)+Γ(a+ε,Z)\gamma(a + \varepsilon, Z) + \Gamma(a + \varepsilon, Z) with an integer Z≈0.55log⁡(2)pZ \approx 0.55 \log(2) p at precision pp, as in arb_hypgeom_gamma_fmpq: the lower series at ZZ and the asymptotic series at ZZ (at reduced precision, since Γ(a+ε,Z)\Gamma(a+\varepsilon, Z) is small) are both evaluated by binary splitting. If the asymptotic series does not converge to the required accuracy (at low precision or for large aa), ZZ is increased until it does, or until the second term is negligible. With len = 1, this calls arb_gamma_fmpq.

Cite this page

The FLINT team, “_arb_hypgeom_gamma_fmpq_jet (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_fmpq_jet.html (generated 2026-11-02).