Necessary and sufficient conditions for a function involving divided differences of the di- and tri-gamma functions to be completely monotonic

Details Necessary and sufficient conditions for a function involving divided differences of the di- and tri-gamma functions to be completely monotonic Necessary and sufficient conditions for a function involving divided differences of the di- and tri-gamma functions to be completely monotonic

2009-03-18

arxiv.org/abs/0903.3071v1

Mathematics

Classical Analysis and ODEs

14 pages

Scientific paper

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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