Further Generalization of the Extended Hurwitz-Lerch Zeta Functions

• Main Authors: Rakesh K. Parmar, Junesang Choi, Sunil Dutt Purohit
• Format: Article
• Language: English
• Published: Sociedade Brasileira de Matemática 2019-01-01
• Series: Boletim da Sociedade Paranaense de Matemática
• Subjects: Generalized Hurwitz-Lerch Zeta function; Extended Beta function; Extended hypergeometric function; Extended Hurwitz-Lerch Zeta function; Mellin Transform; Extended Fractional Derivative Operator
• Online Access: http://periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/31842
• ISSN: 0037-8712; 2175-1188

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.