Whittaker transform

Summary

A Whittaker transform is an integral transform on $(0, \infty)$ whose kernel is built from a Whittaker function $W_{\kappa, \mu}$ of the product $xy$. Several normalizations are in use in the literature. The form recorded here contains the Laplace transform as the special case $\kappa = \mu + 1/2$. Whittaker functions are confluent hypergeometric functions, so these transforms belong to the study of transforms with special function kernels.