On a problem involving the squares of odd harmonic numbers

TL;DR

This paper provides a complete solution to a problem involving series of squared sums of odd harmonic numbers, using advanced techniques from the theory of colored multiple zeta values.

Contribution

It introduces a novel approach employing colored multiple zeta values to solve a longstanding problem about odd harmonic number series.

Findings

Closed-form expressions for the series involving squared sums of odd harmonic numbers.

Application of colored multiple zeta values techniques to harmonic series problems.

Resolution of the problem posed by Wang and Chu.

Abstract

We introduce a full solution to a problem considered by Wang and Chu concerning series involving the squares of finite sums of the form $1 + \frac{1}{3}+ \cdots + \frac{1}{2n-1}$. Our proof involves techniques from the theory of colored multiple zeta values.