On generalized Mathieu series and its companions

Abstract

Integral representations for a generalized Mathieu series and its companions are used to obtain bounds for their corresponding series. The bounds are procured mainly using results pertaining to the Čebyšev functional. The relationship to Zeta type functions are also examined. It is demonstrated that the Zeta companion relations are a particular case of the generalised Mathieu companions.

Keywords

• companion generalized Mathieu series,identities and bounds,Čebyšev functional,Zeta function companion relations

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