Abstract and Applied Analysis
Volume 2013 (2013), Article ID 128458, 6 pages
http://dx.doi.org/10.1155/2013/128458
Research Article

On an Extension of Kummer's Second Theorem

Medhat A. Rakha,1,2 Mohamed M. Awad,2 and Arjun K. Rathie3

1Department of Mathematics and Statistics, College of Science, Sultan Qaboos University, P.O. Box 36 (123), Alkhoud, Muscat, Oman
2Department of Mathematics, Faculty of Science, Suez Canal University, Ismailia 41511, Egypt
3Department of Mathematics, School of Mathematical and Physical Sciences, Central University of Kerala, Riverside Transit Campus, Padennakkad P.O. Nileshwar, Kasaragod, Kerala 671 328, India

Received 4 December 2012; Accepted 26 February 2013

Academic Editor: Adem Kiliçman

Copyright © 2013 Medhat A. Rakha et al. 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

The aim of this paper is to establish an extension of Kummer's second theorem in the form , where . For , we recover Kummer's second theorem. The result is derived with the help of Kummer's second theorem and its contiguous results available in the literature. As an application, we obtain two general results for the terminating series. The results derived in this paper are simple, interesting, and easily established and may be useful in physics, engineering, and applied mathematics.