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Journal of Complex Analysis
Volume 2014, Article ID 820951, 7 pages
http://dx.doi.org/10.1155/2014/820951
Research Article

Summation Formulas Obtained by Means of the Generalized Chain Rule for Fractional Derivatives

Department of Mathematics and Computer Science, University of Quebec at Chicoutimi, QC, Canada G7H 2B1

Received 7 May 2014; Revised 11 August 2014; Accepted 18 August 2014; Published 28 August 2014

Academic Editor: Arcadii Z. Grinshpan

Copyright © 2014 S. Gaboury and R. Tremblay. 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

In 1970, several interesting new summation formulas were obtained by using a generalized chain rule for fractional derivatives. The main object of this paper is to obtain a presumably new general formula. Many special cases involving special functions of mathematical physics such as the generalized hypergeometric functions, the Appell function, and the Lauricella functions of several variables are given.