论文标题
超谐音数的Euler总和的积分表示
Integral representation for Euler sums of hyperharmonic numbers
论文作者
论文摘要
在这篇简短的论文中，我们得出了超谐音数量的Euler总和的积分表示。我们使用其他作者建立的结果来表明积分在第一类的Zeta值和Stirling数字方面具有封闭形式。具体而言，积分具有$$ \ int_0^\ infty \ frac {t^{m-1} \ ln（1-e^{ - t}）} {（1-e^{ - t}）} {（1-e^{ - t} { - t}）
In this short paper, we derive an integral representation for Euler sums of hyperharmonic numbers. We use results established by other authors to then show that the integral has a closed-form in terms of zeta values and Stirling numbers of the first kind. Specifically, the integral has the form of $$\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 $r\ge1$.
