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The evaluation of integrals of Bessel functions via Gfunction identities

Summary: The evaluation of integrals of Bessel functions via
G­function identities
Victor Adamchik
Wolfram Research Inc., 100 Trade Center Dr., Champaign, IL 61820, USA
A few transformations are presented for reducing certain cases of Meijer's G­
function to a G­function of lower order. Their applications to the integration of a
product of Bessel functions are given. The algorithm has been implemented within
Mathematica 3.0.
1 Introduction
In this note we continue to discuss the algorithm of obtaining analytical
solutions to definite integals by using the method of the Mellin integral
transform. The overall idea of this method has been given in Adamchik
and Marichev [2]. It was shown there that by applying the Mellin integral
transform to an improper integral, the latter can be represented by means
of Meijer's G­function, which is, in other words, a Mellin­Barnes contour
integral in the complex plane. The success of this method (at this stage)
depends on two things: first, the Mellin image of a correspondent function
must exist and, second, the Mellin image should be represented in terms of
gamma functions. If these conditions are satisfied, then the next question,


Source: Adamchik, Victor - School of Computer Science, Carnegie Mellon University


Collections: Computer Technologies and Information Sciences