Convolution of Hankel transform and its application to an integral involving Bessel functions of first kind

Vu Kim Tuan,Megumi Saigo

doi:10.1155/s016117129500069x

Abstract

In the paper a convolution of the Hankel transform is constructed. The convolution is used to the calculation of an integral containing Bessel functions of the first kind.

Highlights

The convolution of a modified Hankel transform, introduced in [4], has been studied in [1], [4] in classical sense and in [7] in a space of generalized functions
The present paper is devoted to propose a definition of a convolution and to prove the convolution property in the classical sense of the following standard Hankel transform
It is easy to see that the convolution is a commutative operator of f and g

Summary

Introduction

The convolution of a modified Hankel transform, introduced in [4], has been studied in [1], [4] in classical sense and in [7] in a space of generalized functions. For an another modified Hankel transform the other convolution in some space of functions is obtained (see [5]). The present paper is devoted to propose a definition of a convolution and to prove the convolution property in the classical sense of the following standard Hankel transform (see [6], [8]) As one of its applications, a formula of infinite interval of a product of Bessel functions of the first kind is established.

Results

Conclusion