On an infinite number of new families of odd-type Euler sums

TL;DR

This paper introduces new families of Euler sums involving odd harmonic numbers, computed explicitly using two-valued integer functions and expressed solely in terms of zeta values.

Contribution

It presents novel sequences of Euler sums involving odd harmonic numbers and a new calculational method based on two-valued integer functions.

Findings

Explicit formulas for new Euler sum sequences involving odd harmonic numbers

Representation of these sums solely in terms of zeta values

A calculational technique using two-valued integer functions

Abstract

We present several sequences of Euler sums involving odd harmonic numbers. The calculational technique is based on proper two-valued integer functions, which allow to compute these sequences explicitly in terms of zeta values only.