On the Stieltjes constants with respect to harmonic zeta functions

Series of zeta values , the Stieltjes constants , and a sum

We present a variety of series representations of the Stieltjes and related constants, the Stieltjes constants being the coefficients of the Laurent expansion of the Hurwitz zeta function ζ(s, a) about s = 1. Additionally we obtain series and integral representations of a sum Sγ(n) formed as an alternating binomial series from the Stieltjes constants. The slowly varying sum Sγ(n) + n is an impo...

On Meromorphic Harmonic Functions with Respect to k-Symmetric Points

Geometric Studies on Inequalities of Harmonic Functions in a Complex Field Based on ξ-Generalized Hurwitz-Lerch Zeta Function

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.

Series representations for the Stieltjes constants

The Stieltjes constants γk(a) appear as the coefficients in the regular part of the Laurent expansion of the Hurwitz zeta function ζ(s, a) about s = 1. We present series representations of these constants of interest to theoretical and computational analytic number theory. A particular result gives an addition formula for the Stieltjes constants. As a byproduct, expressions for derivatives of a...

New results on the Stieltjes constants: Asymptotic and exact evaluation

The Stieltjes constants γk(a) are the expansion coefficients in the Laurent series for the Hurwitz zeta function about s = 1. We present new asymptotic, summatory, and other exact expressions for these and related constants.