Necessary and Sufficient Conditions for a Function Involving Divided Differences of the Di- and Tri-gamma Functions to Be Completely Monotonic

نویسنده

  • FENG QI
چکیده

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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تاریخ انتشار 2009