International Journal of Mathematics and Mathematical Sciences
Volume 2012 (2012), Article ID 789519, 16 pages
http://dx.doi.org/10.1155/2012/789519
Research Article

Generalization of a Quadratic Transformation Formula due to Gauss

Medhat A. Rakha1,2

1Department of Mathematics and Statistics, College of Science, Sultan Qaboos University, P.O. Box 36, Alkhodh, Muscat 123, Oman
2Department of Mathematics, Faculty of Science, Suez Canal University, Ismailia, Egypt

Received 19 April 2012; Accepted 12 June 2012

Academic Editor: Hernando Quevedo

Copyright © 2012 Medhat A. Rakha. 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 research paper is to obtain explicit expressions of ( 1 − 𝑥 ) 2 − 2 𝑎 𝐹 1 [ 𝑎 , 𝑏 ; − 4 𝑥 / ( 1 − 𝑥 ) 2 2 𝑏 + 𝑗 ] for 𝑗 = 0 , ± 1 , ± 2 . For 𝑗 = 0 , we have the well-known transformation formula due to Gauss. The results are derived with the help of generalized Watson's theorem. Some known results obtained earlier follow special cases of our main findings.