Authors, define and establish a new subclass of harmonic regular schlicht functions (HSF) in the open unit disc through the use of the extended generalized Noor-type integral operator associated with the ξ-generalized Hurwitz-Lerch Zeta function (GHLZF). Furthermore, some geometric properties of this subclass are also studied.

A new three-dimensional integral containing f(x,y,z)Iv(x?) is derived where Iv(x?) the Modified Bessel Function of first kind and taken over infinite cubic space 0<x<?,0<y<?,0<z<?. The not easily evaluated for complex ranges parameters. representation in terms Hurwitz–Lerch zeta function, polylogarithm function Riemann functions are evaluated. This yields triple representation...

We derive the infinite sum of Lerch function in terms incomplete gamma and function. Special cases are evaluated fundamentals constants. All results this work new.

In this research-cum-expository article, we aim at presenting a systematic account of some recent developments involving the Riemann Zeta function ζ(s), the Hurwitz (or generalized) Zeta function ζ(s, a), and the Hurwitz-Lerch Zeta function Φ(z, s, a) as well as its various interesting extensions and generalizations. In particular, we begin by looking into the problems associated with the evalu...

"In this manuscript, the authors derived a definite integral involving logarithmic function, function of powers and polynomials in terms Lerch function. A summary results is produced form table integrals for easy referencing by readers."

Abstract We explore a recently opened approach to the study of zeta functions, namely fractional calculus. By utilising machinery derivatives and integrals, which have rarely been applied in analytic number theory before, we are able obtain some differential relations finally partial equation type is satisfied by Lerch function.