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.
Junesang Choi, Rakesh Kumar Parmar, and Tibor K. Pog\'any
Dongguk University, Government College of Engineering and Technology, \'Obuda University
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
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