FLINT3.7.0-dev
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acb_hypgeom_bessel_j_0f1

Synopsis#include <flint/acb_hypgeom.h>
void acb_hypgeom_bessel_j_0f1(acb_t res, const acb_t nu, const acb_t z, slong prec)source

Sets res to Jν(z)J_\nu(z) computed from the convergent series

Jν(z)=1Γ(ν+1)(z2)ν0F1(ν+1,−z24),J_{\nu}(z) = \frac{1}{\Gamma(\nu+1)} \left(\frac{z}{2}\right)^{\nu} {}_0F_1\left(\nu+1, -\frac{z^2}{4}\right),

using J−n(z)=(−1)nJn(z)J_{-n}(z) = (-1)^n J_n(z) for negative integer ν\nu.

Cite this page

The FLINT team, “acb_hypgeom_bessel_j_0f1 (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_0f1.html (generated 2026-11-02).