FLINT3.7.0-dev
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acb_hypgeom_bessel_y

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

Sets res to the Bessel function of the second kind

Yν(z)=cos⁡(νπ)Jν(z)−J−ν(z)sin⁡(νπ),Y_{\nu}(z) = \frac{\cos(\nu \pi) J_{\nu}(z) - J_{-\nu}(z)}{\sin(\nu \pi)},

or for ν=n\nu = n an integer the limit

Yn(z)=−2π(inKn(iz)+[log⁡(iz)−log⁡(z)]Jn(z)).Y_n(z) = -\frac{2}{\pi} \left( i^n K_n(iz) + \left[\log(iz)-\log(z)\right] J_n(z) \right).

The output is indeterminate if ν\nu is inexact and contains an integer.

Cite this page

The FLINT team, “acb_hypgeom_bessel_y (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_y.html (generated 2026-11-02).