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

preprint2016arXivOpen access

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.

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

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

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