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arXiv · 2007.01894

Integral representation for Euler sums of hyperharmonic numbers

Casimir Rönnlöf
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Abstract

In this short paper, we derive an integral representation for Euler sums of hyperharmonic numbers. We use results established by other authors to then show that the integral has a closed-form in terms of zeta values and Stirling numbers of the first kind. Specifically, the integral has the form of $$\int_0^\infty \frac{t^{m-1}\ln(1-e^{-t})}{(1-e^{-t})^r} \ dt$$ where $m, r \in \mathbb{N}$, $m > r$ and $r\ge1$.

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Casimir Rönnlöf. 2020-08-06. Integral representation for Euler sums of hyperharmonic numbers. https://arxiv.org/abs/2007.01894

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