International Journal of Mathematics and Mathematical Sciences
Volume 11 (1988), Issue 4, Pages 635-642
doi:10.1155/S0161171288000778

On an integral transform

Abstract

A formula of inversion is established for an integral transform whose kernel is the Bessel function Ju(kr) where r varies over the finite interval (0,a) and the order u is taken to be the eigenvalue parameter. When this parameter is large the Bessel function behaves for varying r like the power function ru and by relating the Bessel functions to their corresponding power functions the proof of the inversion formula can be reduced to one depending on the Mellin inversion theorem.