acb_hypgeom_bessel_j
#include <flint/acb_hypgeom.h>For |z| < 8 the function sums the convergent series. Otherwise it uses the asymptotic expansion if |z| \ge 2^{64} or 2|z| \ge \mathit{prec}, and the convergent series otherwise, with the working precision increased by an estimate (|z| - |\operatorname{Im} z|)/\log 2 of the cancellation (no increase when the terms have equal signs or \nu > |z|^2/4). For inexact input with integer \nu the series is evaluated at the midpoint and the propagated error is bounded with acb_hypgeom_bessel_j_deriv_bound. If the enclosure has less than one bit of accuracy, it is intersected with a direct bound for |J_\nu(z)|.
Guides#
The FLINT team, “acb_hypgeom_bessel_j (acb_hypgeom.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/acb_hypgeom/acb_hypgeom_bessel_j.html (generated 2026-10-20).
@misc{flint-doc-acb-hypgeom-acb-hypgeom-bessel-j,
author = {{The FLINT team}},
title = {{acb\_hypgeom\_bessel\_j (acb\_hypgeom.h)}},
howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
year = {2026},
url = {https://flintlib.org/doc/acb_hypgeom/acb_hypgeom_bessel_j.html},
note = {Generated 2026-10-20}
}