Y transform

Summary

The Y transform of order $\nu$ is an integral transform on $(0, \infty)$ with kernel $\sqrt{xy}\, Y_\nu(xy)$. Here $Y_\nu$ is the Bessel function of the second kind. It is the companion of the Hankel transform, which uses the Bessel function of the first kind $J_\nu$ in the same way. Unlike the Hankel transform, it is not its own inverse. It appears when boundary value problems in cylindrical coordinates need solutions that are singular on the axis.