English

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

Classical Analysis and ODEs 2022-10-27 v1

Abstract

It is proved that (xn1ex)(n)>0\left(\frac{x^n}{1-e^{-x}}\right)^{(n)}>0 for all x(log2,)x\in (\log 2, \infty) and nNn\in \mathbb{N}, which improves the result of [Al-Musallam and Bustoz in Ramanujan J. 11 (2006) 399-402].

Keywords

Cite

@article{arxiv.2210.14693,
  title  = {On the positivity of a certain function related with the Digamma function},
  author = {K. Castillo},
  journal= {arXiv preprint arXiv:2210.14693},
  year   = {2022}
}
R2 v1 2026-06-28T04:33:14.441Z