Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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On Extended Hurwitz-Lerch Zeta Function

  • Received : 2022.08.07
  • Accepted : 2023.02.22
  • Published : 2023.09.30
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Abstract

This paper investigates an extended form Hurwitz-Lerch zeta function, as well as related integral images, ordinary and fractional derivatives, and series expansions, using the term extended beta function. We establish a connection between the extended Hurwitz-Lerch zeta function and the Laguerre polynomials. Furthermore, we present a probability distribution application of the extended Hurwitz-Lerch zeta function ζ𝛿,𝜇𝜈,λ. Several results, both known and new, are shown to follow as special cases of our findings.

Keywords

Acknowledgement

We appreciate the anonymous reviewers insightful comments, which improved the readability of the papers presentation.

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