On Mathieu-Type Series with (p,ν)-Extended Hypergeometric Terms: Integral Representations and Upper Bounds - Rakesh K. Parmar; Tibor K. Pogány; S. Saravanan (Mathematics, 2023)
Integral form expressions are obtained for the Mathieu-type series and for their associated alternating versions, the terms of which contain a <semantics>(p,ν)</semantics>-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.