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arXiv · 2210.14693

On the positivity of a certain function related with the Digamma function

K. Castillo
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Abstract

It is proved that $$\left(\frac{x^n}{1-e^{-x}}\right)^{(n)}>0$$ for all $x\in (\log 2, \infty)$ and $n\in \mathbb{N}$, which improves the result of [Al-Musallam and Bustoz in Ramanujan J. 11 (2006) 399-402].

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K. Castillo. 2022-10-26. On the positivity of a certain function related with the Digamma function. https://arxiv.org/abs/2210.14693

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