acb_hypgeom_bessel_k_0f1_series
Synopsis
#include <flint/acb_hypgeom.h>void acb_hypgeom_bessel_k_0f1_series(acb_poly_t res, const acb_poly_t nu, const acb_poly_t z, int scaled, slong len, slong prec)sourceSets res to K_\nu(z) (or e^z K_\nu(z) if scaled is nonzero) as a power series truncated to length len, for power series \nu, z \in \mathbb{C}[[x]], using
K_{\nu}(z) = \frac{1}{2} \frac{\pi}{\sin(\pi \nu)} \left[
\left(\frac{z}{2}\right)^{-\nu}
{}_0{\widetilde F}_1\left(1-\nu, \frac{z^2}{4}\right) -
\left(\frac{z}{2}\right)^{\nu}
{}_0{\widetilde F}_1\left(1+\nu, \frac{z^2}{4}\right) \right].
If the constant term of \nu is an integer, one extra derivative is computed and the singularity is removed (the coefficient of x in \nu must then be nonzero). The output is indeterminate if the constant term of \nu is inexact and contains an integer.
Cite this page
The FLINT team, “acb_hypgeom_bessel_k_0f1_series (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_series.html (generated 2026-10-20).
@misc{flint-doc-acb-hypgeom-acb-hypgeom-bessel-k-0f1-series,
author = {{The FLINT team}},
title = {{acb\_hypgeom\_bessel\_k\_0f1\_series (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_series.html},
note = {Generated 2026-10-20}
}