Hypergeometric type extended bivariate zeta function

Based on the generalized extended beta function, we shall introduce and study a new hypergeometric-type extended zeta function together with related integral representations, differential relations, finite sums, and series expansions. Also, we present a relationship between the extended zeta functio...

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Bibliographic Details
Published in:Tamkang journal of mathematics 2024-03
Main Authors: Pathan, M. A., Shahwan, Mohannad, Bin-Saad, Maged Gumman
Format: Article
Language:English
Online Access:Get full text
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Summary:Based on the generalized extended beta function, we shall introduce and study a new hypergeometric-type extended zeta function together with related integral representations, differential relations, finite sums, and series expansions. Also, we present a relationship between the extended zeta function and the Laguerre polynomials. Our hypergeometric type extended zeta function involves several known zeta functions including the Riemann, Hurwitz, Hurwitz-Lerch, and Barnes zeta functions as particular cases.
ISSN:0049-2930
2073-9826
DOI:10.5556/j.tkjm.55.2024.5120