Open Access
Translator Disclaimer
2013 On an Extension of Kummer's Second Theorem
Medhat A. Rakha, Mohamed M. Awad, Arjun K. Rathie
Abstr. Appl. Anal. 2013(SI50): 1-6 (2013). DOI: 10.1155/2013/128458

Abstract

The aim of this paper is to establish an extension of Kummer's second theorem in the form e - x / 2 F 2 2 [ a , 2 + d ; x 2 a + 2 , d ; ] = F 1 0 [ - ; x 2 / 16 a + 3 / 2 ; ] + ( ( a / d - 1 / 2 ) / ( a + 1 ) ) x F 1 0 [ - ; x 2 / 16 a + 3 / 2 ; ] + ( c x 2 / 2 ( 2 a + 3 ) ) F 1 0 [ - ; x 2 / 16 a + 5 / 2 ; ] , where   c = 1 / a + 1 1 / 2 - a / d + a / d ( d + 1 ) , d 0 , - 1 , - 2 , . For d = 2 a , 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 F 2 3 ( 2 ) series. The results derived in this paper are simple, interesting, and easily established and may be useful in physics, engineering, and applied mathematics.

Citation

Download Citation

Medhat A. Rakha. Mohamed M. Awad. Arjun K. Rathie. "On an Extension of Kummer's Second Theorem." Abstr. Appl. Anal. 2013 (SI50) 1 - 6, 2013. https://doi.org/10.1155/2013/128458

Information

Published: 2013
First available in Project Euclid: 26 February 2014

zbMATH: 1277.33008
MathSciNet: MR3039181
Digital Object Identifier: 10.1155/2013/128458

Rights: Copyright © 2013 Hindawi

JOURNAL ARTICLE
6 PAGES


SHARE
Vol.2013 • No. SI50 • 2013
Back to Top