Communications in Numerical Analysis

Volume 2016, No. 1 (2016), Pages 50-56

Article ID cna-00244, 7 Pages

doi: 10.5899/2016/cna-00244


Research Article


Certain new unified integrals associated with the product of generalized Bessel functions


Praveen Agarwal1 *, Daniele Ritelli2, Adem Kilicman3, Shilpi Jain4


1Department of Mathematics, Anand International College of Engineering, Jaipur-303012, India.

2School of Economics, Management and Statistics, Dipartimento di Scienze Statistiche, University of Bologna, via Belle Arti 41, 40126 Bologna Italy.

3Universiti Putra Malaysia, Department of Mathematics, Serdang, Malaysia.

4Department of Mathematics, Poornima College of Engineering, Jaipur-303012, India.


* Corresponding author. Email address: goyal.praveen2011@gmail.com; Tel:+91 8387894656.


Received: 02 June 2015; Revised: 18 August 2015; Accepted: 28 October 2015


Copyright © 2016 Praveen Agarwal, Daniele Ritelli, Adem Kilicman and Shilpi Jain. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Our focus to presenting two very general integral formulas whose integrands are the integrand given in the Oberhettinger's integral formula and a finite product of the generalized Bessel function of the first kind, which are expressed in terms of the generalized Lauricella functions. Among a large number of interesting and potentially useful special cases of our main results, some integral formulas involving such elementary functions are also considered.


Keywords: Gamma function; Generalized hypergeometric function ${

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