Elsevier

Journal of Number Theory

Volume 130, Issue 2, February 2010, Pages 360-369
Journal of Number Theory

Hyperharmonic series involving Hurwitz zeta function

https://doi.org/10.1016/j.jnt.2009.08.005Get rights and content
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Abstract

We show that the sum of the series formed by the so-called hyperharmonic numbers can be expressed in terms of the Riemann zeta function. These results enable us to reformulate Euler's formula involving the Hurwitz zeta function. In additon, we improve Conway and Guy's formula for hyperharmonic numbers.

MSC

11B83

Keywords

Hyperharmonic numbers
Euler sums
Riemann zeta function
Hurwitz zeta function
Hypergeometric series

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