Some series and integrals involving the Riemann zeta function, binomial coefficients and the harmonic numbers. Volume II(b)

TL;DR

This paper presents elementary analysis-based identities involving the Riemann zeta function, binomial coefficients, and harmonic numbers, contributing new formulas and expository insights into these mathematical relationships.

Contribution

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

Findings

Several new identities involving the Riemann zeta function

Elementary derivations of complex series and integrals

Enhanced understanding of harmonic numbers and binomial coefficients

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.