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

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.