CONVOLUTION OF HANKEL TRANSFORM AND ITS APPLICATION TO AN INTEGRAL INVOLVING BESSEL FUNCTIONS OF FIRST KIND vu

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.


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]) yJ(yx)f(y)dy, Re(,) > (1) As one of its applications, a formula of infinite interval of a product of Bessel functions of the first kind is established.

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The function h(x) is called the Hankel convolution of the function f(x) with the function g(x).It is easy to see that the convolution is a commutative operator of f and g.
Let L(R+;p.(x))be a class of integrable functions f(x) with a weight p(x) > 0 in R + (0, oo).
The main aim of this section is to prove the following: and there hoils the convolution property 9 where :f,, is the Hankel transform (1).

Call for Papers
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