English

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.

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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}
}

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14 pages