A note on some integrals used in laser field

involving the product of Bessel functions

 

A. Belafhal*, S. Hennani

Laboratoire de Physique Nucléaire, Atomique et Moléculaire,

Département de Physique, Faculté des Sciences, Université Chouaïb Doukkali

B.P. 20, El Jadida 24000, Morocco

* Corresponding author. E-mail:  belafhal@gmail.com

Received: 30 July 2011; revised version accepted: 22 September 2011

 

Abstract

     A closed form expression in terms of the Humbert’s confluent hypergeometric function of two variables Psi1 is derived for the integral involving the product of two Bessel functions.

Some alternative derivations are indicated in the cases of some integral formulas corresponding to two special values of Bessel functions of integer and fractional orders, the results are believed to be new.

 

Keywords : Bessel function; Modified Bessel function; Gamma function; Humbert’s confluent hypergeometric function.

 

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