# IJPAM: Volume 55, No. 2 (2009)

THE HANKEL CONVOLUTION OF ARBITRARY ORDER

C.K. Li
Department of Mathematics and Computer Science
Brandon University
e-mail: lic@brandonu.ca

Abstract.Let . The classical Hankel transform is defined by

 (1)

where denotes the Bessel function of the first kind and order . The goal of this paper is to construct the Hankel transform of arbitrary order based on the two differential operators and show that on for . Further more, the Hankel convolution of arbitrary order is introduced with the following identity

on the spaces and respectively.

AMS Subject Classification: 46F12

Key Words and Phrases: Hankel transform, Bessel function, Hankel convolution and automorphism

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 55
Issue: 2