About this Journal Submit a Manuscript Table of Contents
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

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.

Linked References

  1. Y. S. Kim, M. A. Rakha, and A. K. Rathie, “Generalizations of Kummer's second theorem with application,” Journal of Computational Mathematics and Mathematical Physics, vol. 50, no. 3, pp. 387–402, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  2. Y. S. Kim, M. A. Rakha, and A. K. Rathie, “Extensions of certain classical summation theorems for the series 2F1, 3F2, and 4F3 with applications in Ramanujan's summations,” International Journal of Mathematics and Mathematical Sciences, vol. 2010, Article ID 309503, 26 pages, 2010. View at Publisher · View at Google Scholar · View at Scopus
  3. M. A. Rakha and A. K. Rathie, “Generalizations of classical summation theorems for the series 2F1 and 3F2 with applications,” Integral Transforms and Special Functions, vol. 22, no. 11, pp. 823–840, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. W. N. Bailey, “Products of generalized hypergeometric series,” Proceedings of the London Mathematical Society, vol. 28, no. 1, pp. 242–250, 1928. View at Publisher · View at Google Scholar · View at MathSciNet
  5. E. E. Kummer, “Über die hypergeometridche Reihe,” Journal für Die Reine Und Angewandte Mathematik, vol. 15, pp. 39–83, 1836.
  6. J. Choi and A. K. Rathie, “Another proof of Kummer's second theorem,” Communications of the Korean Mathematical Society, vol. 13, no. 4, pp. 933–936, 1998. View at Zentralblatt MATH · View at MathSciNet
  7. E. D. Rainville, Special Functions, The Macmillan Company, New York, NY, USA, 1960. View at MathSciNet
  8. A. K. Rathie and V. Nagar, “On Kummer's second theorem involving product of generalized hypergeometric series,” Le Matematiche, vol. 50, no. 1, pp. 35–38, 1995. View at Zentralblatt MATH · View at MathSciNet
  9. J.-L. Lavoie, F. Grondin, and A. K. Rathie, “Generalizations of Watson's theorem on the sum of a 3F2,” Indian Journal of Mathematics, vol. 34, no. 1, pp. 23–32, 1992. View at Zentralblatt MATH · View at MathSciNet
  10. A. K. Rathie and T. K. Pogány, “New summation formula for 3F2(1/2) and a Kummer-type II transformation of 2F2(x),” Mathematical Communications, vol. 13, no. 1, pp. 63–66, 2008. View at Zentralblatt MATH · View at MathSciNet
  11. M. A. Rakha, “A note on Kummer-type II transformation for the generalized hypergeometric function 2F2,” Mathematical Notes, vol. 19, no. 1, pp. 154–156, 2012.
  12. Y. S. Kim, J. Choi, and A. K. Rathie, “Two results for the terminating 3F2(2) with applications,” Bulletin of the Korean Mathematical Society, vol. 49, no. 3, pp. 621–633, 2012. View at Publisher · View at Google Scholar · View at MathSciNet