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arXiv · 2103.11876

On Evaluations of Euler-type Sums of Hyperharmonic Numbers

Levent Kargın·Mümün Can·Ayhan Dil·Mehmet Cenkci
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Abstract

We give explicit evaluations of the linear and non-linear Euler sums of hyperharmonic numbers $h_{n}^{\left( r\right) }$ with reciprocal binomial coefficients. These evaluations enable us to extend closed form formula of Euler sums of hyperharmonic numbers to an arbitrary integer $r$. Moreover, we reach at explicit formulas for the shifted Euler-type sums of harmonic and hyperharmonic numbers. All the evaluations are provided in terms of the Riemann zeta values, harmonic numbers and linear Euler sums.

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Levent Kargın, Mümün Can, Ayhan Dil, Mehmet Cenkci. 2021-03-22. On Evaluations of Euler-type Sums of Hyperharmonic Numbers. https://arxiv.org/abs/2103.11876

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