FLINT3.7.0-dev
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_arb_gamma_upper_fmpq_step_bsplit_jet

Synopsis#include <flint/arb_hypgeom.h>
void _arb_gamma_upper_fmpq_step_bsplit_jet(arb_ptr Gz1, const fmpq_t a, const arb_t z0, const arb_t logz0, const arb_t z1, arb_srcptr Gz0, const arb_t expmz0, const mag_t abs_tol, slong len, slong prec)source

Jet version of _arb_gamma_upper_fmpq_step_bsplit: given the jet Gz0 of Γ(a+ε,z0)\Gamma(a + \varepsilon, z_0) and expmz0 containing e−z0e^{-z_0}, sets Gz1 to the jet of Γ(a+ε,z1)\Gamma(a + \varepsilon, z_1). The matrix binary splitting is done with power series entries. The truncation error is bounded using Cauchy estimates on a circle of radius RR around z0z_0, with an extra factor max⁡j<lenΛj/j!\max_{j < \text{len}} \Lambda^j / j! where Λ\Lambda bounds ∣log⁡(t)∣|\log(t)| on the circle; the radius RR is chosen with this factor taken into account.

Cite this page

The FLINT team, “_arb_gamma_upper_fmpq_step_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_gamma_upper_fmpq_step_bsplit_jet.html (generated 2026-11-02).