Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

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Bull. Korean Math. Soc. 2017; 54(3): 789-797

Online first article November 3, 2016      Printed May 31, 2017

https://doi.org/10.4134/BKMS.b160313

Copyright © The Korean Mathematical Society.

Mathieu-type series built by $(p, q)$--extended Gaussian hypergeometric function

Junesang Choi, Rakesh Kumar Parmar, and Tibor K. Pog\'any

Dongguk University, Government College of Engineering and Technology, \'Obuda University

Abstract

The main purpose of this paper is to present closed integral form expressions for the Mathieu-type $\boldsymbol a$-series and its associated alternating version whose terms contain a $(p, q)$--extended Gauss' hypergeometric function. Certain upper bounds for the two series are also given.

Keywords: $(p, q)$-extended Beta function, $(p, q)$-extended Gaussian hypergeometric function, integral representations, Mathieu--type series, Cahen formula, bounding inequality

MSC numbers: Primary 33B20, 33C20; Secondary 33B15, 33C05