Four types of variant Euler harmonic sums

TL;DR

This paper investigates four types of variant Euler harmonic sums, providing new evaluations and exploring their connections to zeta functions and known mathematical constants.

Contribution

It introduces a comprehensive analysis of four variant Euler harmonic sums and links them to established mathematical functions and constants.

Findings

Explicit evaluations of variant Euler harmonic sums

Connections to zeta functions and mathematical constants

Examples illustrating the sums' relationships to known series

Abstract

We aim to investigate the four types of variant Euler harmonic sums. Also, as corollaries, we provide particular examples of our core findings, some of whose further instances are evaluated in terms of basic and well-known functions as well as certain mathematical constants. We explore relevant linkages between our results and those of other previously established studies. An examination of a specific case of one result shows a relationship to series involving zeta functions, which is also a popular area of research.