Some series and integrals involving the Riemann zeta function, binomial coefficients and the harmonic numbers. Volume III

TL;DR

This paper presents elementary analysis-based identities involving the Riemann zeta function, binomial coefficients, and harmonic numbers, contributing new formulas and insights in a mainly expository series.

Contribution

It introduces new identities related to the Riemann zeta function derived through elementary methods, enriching the mathematical understanding of these functions.

Findings

Several new identities involving the Riemann zeta function

Elementary derivations of complex formulas

Compilation of related series and integrals

Abstract

In this series of seven papers, predominantly by means of elementary analysis, we establish a number of identities related to the Riemann zeta function. Whilst this paper is mainly expository, some of the formulae reported in it are believed to be new, and the paper may also be of interest specifically due to the fact that most of the various identities have been derived by elementary methods.