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.

Keywords

• (<i>p</i>,<i>ν</i>)-extended Beta function
• (<i>p</i>,<i>ν</i>)-extended Gauss hypergeometric function
• (<i>p</i>,<i>ν</i>)-extended confluent hypergeometric function
• (<i>p</i>,<i>ν</i>)-extended Mathieu-type series
• modified Bessel function of the second kind
• bounding inequalities for (<i>p</i>,<i>ν</i>)-extended Mathieu-type series