FLINT3.7.0-dev
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_arb_hypgeom_gamma_upper_singular_si_choose_N_jet, _arb_hypgeom_gamma_upper_singular_si_bsplit_jet

Synopsis#include <flint/arb_hypgeom.h>
slong _arb_hypgeom_gamma_upper_singular_si_choose_N_jet(mag_t err, slong n, const arb_t z, const mag_t abs_tol, slong len)source
void _arb_hypgeom_gamma_upper_singular_si_bsplit_jet(arb_ptr res, slong n, const arb_t z, const arb_t logz, slong N, arb_srcptr gamma1, slong len, slong prec)source

Jet versions of _arb_hypgeom_gamma_upper_singular_si_choose_N and _arb_hypgeom_gamma_upper_singular_si_bsplit, computing the jet of Γ(−n+ε,z)\Gamma(-n + \varepsilon, z) for an integer n≥0n \ge 0. This uses

Γ(−n+ε,z)=(−1)nn!1ε[Γ(1+ε)∏i=1n(1−ε/i)−zε]−z−n+ε∑k≠n(−z)kk!(k−n+ε).\Gamma(-n + \varepsilon, z) = \frac{(-1)^n}{n!} \frac{1}{\varepsilon}\left[\frac{\Gamma(1+\varepsilon)}{\prod_{i=1}^n (1 - \varepsilon/i)} - z^{\varepsilon}\right] - z^{-n+\varepsilon} \sum_{k \ne n} \frac{(-z)^k}{k! (k - n + \varepsilon)}.

If gamma1 is not NULL, it should contain the jet of Γ(1+ε)\Gamma(1 + \varepsilon) of length len + 1; otherwise this is computed internally.

Cite this page

The FLINT team, “_arb_hypgeom_gamma_upper_singular_si_choose_N_jet, _arb_hypgeom_gamma_upper_singular_si_bsplit_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_upper_singular_si_choose_N_jet.html (generated 2026-11-02).