Necessary and sufficient conditions for a function involving divided differences of the di- and tri-gamma functions to be completely monotonic
Classical Analysis and ODEs
2016-06-30 v1
Abstract
In the present paper, necessary and sufficient conditions are established for a function involving divided differences of the digamma and trigamma functions to be completely monotonic. Consequently, necessary and sufficient conditions are derived for a function involving the ratio of two gamma functions to be logarithmically completely monotonic, and some double inequalities are deduced for bounding divided differences of polygamma functions.
Keywords
Cite
@article{arxiv.0903.3071,
title = {Necessary and sufficient conditions for a function involving divided differences of the di- and tri-gamma functions to be completely monotonic},
author = {Feng Qi and Bai-Ni Guo},
journal= {arXiv preprint arXiv:0903.3071},
year = {2016}
}
Comments
14 pages