FLINT3.7.0-dev
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acb_hypgeom_bessel_k_asymp

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

Sets res to the modified Bessel function of the second kind

Kν(z)=(2zπ)−1/2e−zU∗(ν+12,2ν+1,2z),K_{\nu}(z) = \left(\frac{2z}{\pi}\right)^{-1/2} e^{-z} U^{*}(\nu+\tfrac{1}{2}, 2\nu+1, 2z),

valid for all ν\nu and z≠0z \ne 0, using acb_hypgeom_u_asymp; or ezKν(z)e^z K_\nu(z) if scaled is nonzero.

Cite this page

The FLINT team, “acb_hypgeom_bessel_k_asymp (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_asymp.html (generated 2026-11-02).