Integral representations of equally positive integer-indexed harmonic sums at infinity

TL;DR

This paper introduces a partition-theoretic generalization of the Riemann zeta function and harmonic sums at infinity, providing their generating functions and integral representations, which coincide with known zeta values at positive integers.

Contribution

It presents a novel partition-theoretic framework for harmonic sums and zeta functions, deriving new integral representations and generating functions.

Findings

Derived integral representations for generalized harmonic sums

Established connections with zeta values at positive integers

Provided a partition-theoretic perspective on zeta functions

Abstract

We identify a partition-theoretic generalization of Riemann zeta function and the equally positive integer-indexed harmonic sums at infinity, to obtain the generating function and the integral representations of the latter. The special cases coincide with zeta values at positive integer arguments.