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On Mathieu-Type Series with (p,ν)-Extended Hypergeometric Terms: Integral Representations and Upper Bounds

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Integral form expressions are obtained for the Mathieu-type series and for their associated alternating versions, the terms of which contain a (p,ν)-extended Gauss hypergeometric function. Contiguous recurrence relations are found… Click to show full abstract

Integral form expressions are obtained for the Mathieu-type series and for their associated alternating versions, the terms of which contain a (p,ν)-extended Gauss hypergeometric function. Contiguous recurrence relations are found for the Mathieu-type series with respect to two parameters, and finally, particular cases and related bounding inequalities are established.

Keywords: mathieu type; type series; hypergeometric terms; series extended; extended hypergeometric

Journal Title: Mathematics
Year Published: 2023

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