Summation of Hyperharmonic Series
Istv\'an Mez\H{o}

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.
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Taxonomy
TopicsAdvanced Mathematical Identities · Advanced Combinatorial Mathematics · Analytic Number Theory Research
