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Dirichlet Beta Function via Generalized Mathieu Series Family

In: Frontiers in Functional Equations and Analytic Inequalities

Author

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  • P. Cerone

    (La Trobe University, Department of Mathematics and Statistics)

Abstract

Integral representations for a generalized Mathieu series and its companions are used to obtain approximation and bounds for undertaking analysis leading to novel insights for the Dirichlet Beta function and its companions. The bounds are procured using a variety of approaches including utilizing integral representation and Čebyšev functional results. The relationship to Zeta type functions is also examined. It is demonstrated that the Dirichlet Beta function relations are particular cases of the generalized Mathieu companions.

Suggested Citation

  • P. Cerone, 2019. "Dirichlet Beta Function via Generalized Mathieu Series Family," Springer Books, in: George A. Anastassiou & John Michael Rassias (ed.), Frontiers in Functional Equations and Analytic Inequalities, pages 613-649, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-28950-8_31
    DOI: 10.1007/978-3-030-28950-8_31
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