Further Generalization of the Extended Hurwitz-Lerch Zeta Functions
DOI:
https://doi.org/10.5269/bspm.v37i1.31842Keywords:
Generalized Hurwitz-Lerch Zeta function, Extended Beta function, Extended hypergeometric function, Extended Hurwitz-Lerch Zeta function, Mellin Transform, Extended Fractional Derivative OperatorAbstract
Recently various extensions of Hurwitz-Lerch Zeta functions have been investigated. Here, we first introduce a further generalization of the extended Hurwitz-Lerch Zeta functions. Then we investigate certain interesting and (potentially) useful properties, systematically, of the generalization of the extended Hurwitz-Lerch Zeta functions, for example, various integral representations, Mellin transform, generating functions and extended fractional derivatives formulas associated with these extended generalized Hurwitz-Lerch Zeta functions. An application to probability distributions is further considered. Some interesting special cases of our main results are also pointed out.
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