On harmonic sums and alternating Euler sums

TL;DR

This paper explores the relationship between harmonic sums and alternating Euler sums, providing explicit formulas and evaluations that deepen understanding of their mathematical connections.

Contribution

It introduces explicit formulas connecting harmonic sums with alternating Euler sums, offering new tools for their evaluation and analysis.

Findings

Explicit formulas relating harmonic sums to alternating Euler sums

New evaluations of specific sums using these formulas

Enhanced understanding of the structure of colored multiple zeta values

Abstract

The explicit formulas expressing harmonic sums via alternating Euler sums (colored multiple zeta values) are given, and some explicit evaluations are given as applications.