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

Source: [On the positivity of a certain function related with the Digamma function](<https://www.sota2.com/research/paper/68fa59bb1e209131ce9b99c9>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-27T05:24:35.209Z

Authors: K. Castillo

Published: 2022-10-26T13:23:40.000Z

## 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 \[Al-Musallam and Bustoz in Ramanujan J. 11 (2006) 399-402\].

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2210.14693>)

[PDF](<https://arxiv.org/pdf/2210.14693.pdf>)