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arXiv · 0903.3071

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

Feng Qi·Bai-Ni Guo
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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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Feng Qi, Bai-Ni Guo. 2009-03-18. Necessary and sufficient conditions for a function involving divided differences of the di- and tri-gamma functions to be completely monotonic. https://doi.org/10.1515/gmj-2016-0004

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