acb_hypgeom_bessel_k_0f1
Synopsis
#include <flint/acb_hypgeom.h>void acb_hypgeom_bessel_k_0f1(acb_t res, const acb_t nu, const acb_t z, int scaled, slong prec)sourceSets res to K_\nu(z) (or e^z K_\nu(z) if scaled is nonzero) computed from
K_{\nu}(z) = \frac{1}{2} \left[
\left(\frac{z}{2}\right)^{-\nu} \Gamma(\nu)
{}_0F_1\left(1-\nu, \frac{z^2}{4}\right) -
\left(\frac{z}{2}\right)^{\nu}
\frac{\pi}{\nu \sin(\pi \nu) \Gamma(\nu)}
{}_0F_1\left(\nu+1, \frac{z^2}{4}\right) \right]
for \nu \notin \mathbb{Z}, and the limit computed with acb_hypgeom_bessel_k_0f1_series for \nu \in \mathbb{Z}. The output is indeterminate if \nu is inexact and contains an integer.
Cite this page
The FLINT team, “acb_hypgeom_bessel_k_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_k_0f1.html (generated 2026-10-20).
@misc{flint-doc-acb-hypgeom-acb-hypgeom-bessel-k-0f1,
author = {{The FLINT team}},
title = {{acb\_hypgeom\_bessel\_k\_0f1 (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_k_0f1.html},
note = {Generated 2026-10-20}
}