A REMARK ON THE ZERO ORDER HANKEL TRANSFORM

Pierre Hillion(France)

Received January 16, 2009

Abstract

We prove that for  when m is a positive integer, the zero order Hankel transform of  is a Dirac distribution. As an application, we discuss the Green function of the Helmholtz equation in spherical geometry. We also present the Hankel transform of some Bessel and Gaussian functions obtained from Weber integrals of Bessel functions.

Keywords and phrases: Hankel transform, Bessel function, Dirac distribution.