Abstract This paper deals with the fractional calculus of zeta functions. In particular, study is focused on Hurwitz ? \zeta function. All results are based complex generalization Grünwald-Letnikov derivative. We state and prove functional equation together an integral representation by Bernoulli numbers. Moreover, we ...

Liouville's fractional integration is used to de ne polygamma functions (z) for negative integer n. It's shown that such (z) can be represented in a closed form by means of the rst derivatives of the Hurwitz Zeta function. Relations to the Barnes G-function and generalized Glaisher's constants are also discussed.

We express explicitly the analytic torsion functions associated with Rumin complex on lens spaces in terms of Hurwitz zeta function. In particular, we find that vanish at origin and determine torsions. Moreover, have a formula between this Ray-Singer torsion.

This paper extends tools developed by Richard Crandall in [16] to provide robust, high-precision methods for computation of the incomplete Gamma function and the Lerch transcendent. We then apply these to the corresponding computation of the Hurwitz zeta function and so of Dirichlet L-series and character polylogarithms.

This paper employs a contour integral method to derive and evaluate the infinite sum of Euler polynomial expressed in terms Hurwitz Zeta function. We provide formulae for several classes sums Riemann function fundamental mathematical constants, including Catalan’s constant. representation constant suggests it could be rational.

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