_arb_hypgeom_bessel_j_series, arb_hypgeom_bessel_j_series
#include <flint/arb_hypgeom.h>void _arb_hypgeom_bessel_j_series(arb_ptr res, const arb_t nu, arb_srcptr z, slong zlen, slong len, slong prec)sourcevoid arb_hypgeom_bessel_j_series(arb_poly_t res, const arb_t nu, const arb_poly_t z, slong len, slong prec)sourceSets res to J_\nu(z) for the constant \nu and the power series z, truncated to length len.
Both functions call the generic _gr_poly_bessel_j_series with a real ball context. It computes the Taylor coefficients of J_\nu at the constant term z_0 of z with gr_bessel_j_jet, from J_\nu(z_0), J_{\nu \pm 1}(z_0) and a recurrence derived from the Bessel differential equation, and composes them with z - z_0. The recurrence divides by z_0^2, so the result is indeterminate if z_0 is an inexact ball containing zero; for z_0 = 0 exactly and an integer \nu the coefficients are computed directly.
The FLINT team, “_arb_hypgeom_bessel_j_series, arb_hypgeom_bessel_j_series (arb_hypgeom.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/arb_hypgeom/_arb_hypgeom_bessel_j_series.html (generated 2026-10-20).
@misc{flint-doc-arb-hypgeom-arb-hypgeom-bessel-j-series,
author = {{The FLINT team}},
title = {{\_arb\_hypgeom\_bessel\_j\_series, arb\_hypgeom\_bessel\_j\_series (arb\_hypgeom.h)}},
howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
year = {2026},
url = {https://flintlib.org/doc/arb_hypgeom/_arb_hypgeom_bessel_j_series.html},
note = {Generated 2026-10-20}
}