Limit Representations of Riemann's Zeta Function

TL;DR

The paper presents two new limit representations of Riemann's zeta function for complex numbers with real part greater than one, derived using classical series limit theorems.

Contribution

It introduces two novel limit representations of the zeta function using elementary arguments and Tannery's theorem.

Findings

Two limit representations of ζ(s) for Re(s)>1

Representation derivations based on classical series limit theorems

Simplified proofs of known properties

Abstract

In this paper it is shown that Riemann's zeta function $\zeta(s)$ admits two limit representations when $\Re{(s)}>1.$ Each of these limit representations is deduced by using simple arguments based upon the classical Tannery's (limiting) theorem for series.