• Kyungpook Mathematical Journal
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• v.63 no.3
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• pp.485-506
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• 2023

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 ζ^𝛿,𝜇_𝜈,λ. Several results, both known and new, are shown to follow as special cases of our findings.