Summation of Hyperharmonic Series

TL;DR

This paper derives a formula expressing the sum of hyperharmonic series in terms of the Riemann zeta function, providing a new analytical connection between these mathematical concepts.

Contribution

It introduces a summation formula for hyperharmonic series expressed through the Riemann zeta function, advancing the understanding of hyperharmonic numbers.

Findings

Sum of hyperharmonic series expressed via Riemann zeta function

Provides a general summation formula for hyperharmonic series

Establishes a new analytical link between hyperharmonic numbers and zeta function

Abstract

We shall show that the sum of the series formed by the so-called hyperharmonic numbers can be expressed in terms of the Riemann zeta function. More exactly, we give summation formula for the general hyperharmonic series.