Dirichlet Beta Function via Generalized Mathieu Series Family

Autor:	Pietro Cerone
Rok vydání:	2019
Předmět:	Pure mathematics Integral representation Series (mathematics) Dirichlet beta function Mathematics::Spectral Theory Variety (universal algebra) Type (model theory) Mathematics
Zdroj:	Frontiers in Functional Equations and Analytic Inequalities ISBN: 9783030289492
DOI:	10.1007/978-3-030-28950-8_31
Popis:	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 Cebysev 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.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::58c7b8fddaa104968442780a8a6616a9 https://doi.org/10.1007/978-3-030-28950-8_31 Zobrazit plný text záznamu