A special constant and series with zeta values and harmonic numbers

TL;DR

This paper explores a special mathematical constant linked to series involving harmonic numbers, zeta values, and logarithms, providing new closed-form evaluations of related numerical and power series.

Contribution

It introduces a specific constant and derives closed-form expressions for various series involving harmonic numbers and zeta functions.

Findings

Identification of a new mathematical constant.

Closed-form evaluations of series involving harmonic numbers.

Insights into relationships between harmonic numbers, zeta values, and logarithms.

Abstract

In this paper we demonstrate the importance of a mathematical constant which is the value of several interesting numerical series involving harmonic numbers, zeta values, and logarithms. We also evaluate in closed form a number of numerical and power series.