Mathematics (Apr 2023)
On Mathieu-Type Series with (<i>p</i>,<i>ν</i>)-Extended Hypergeometric Terms: Integral Representations and Upper Bounds
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.
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