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 Mathieu-type series built by $(p, q)$--extended Gaussian hypergeometric function Bull. Korean Math. Soc. 2017 Vol. 54, No. 3, 789-797 https://doi.org/10.4134/BKMS.b160313Published online May 31, 2017 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 Full-Text :