FLINT3.7.0-dev
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_arb_hypgeom_gamma_upper_fmpq_inf_choose_N_jet, _arb_hypgeom_gamma_upper_fmpq_inf_bsplit_jet

Synopsis#include <flint/arb_hypgeom.h>
slong _arb_hypgeom_gamma_upper_fmpq_inf_choose_N_jet(mag_t err, const fmpq_t a, const arb_t z, const mag_t abs_tol, slong len)source
void _arb_hypgeom_gamma_upper_fmpq_inf_bsplit_jet(arb_ptr res, const fmpq_t a, const arb_t z, const arb_t logz, slong N, slong len, slong prec)source

Jet versions of _arb_hypgeom_gamma_upper_fmpq_inf_choose_N and _arb_hypgeom_gamma_upper_fmpq_inf_bsplit. The truncation error (a−1)⋯(a−N)Γ(a−N,z)(a-1)\cdots(a-N) \Gamma(a-N,z) is bounded using majorants for the polynomial factor and for ∫z∞ta−N−1e−tlog⁡j(t)/j! dt\int_z^{\infty} t^{a-N-1} e^{-t} \log^j(t) / j! \, dt. The choose_N function requires z≥1z \ge 1 (otherwise it returns −1-1).

Cite this page

The FLINT team, “_arb_hypgeom_gamma_upper_fmpq_inf_choose_N_jet, _arb_hypgeom_gamma_upper_fmpq_inf_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_fmpq_inf_choose_N_jet.html (generated 2026-11-02).