Necessary and Sufficient Conditions for a Function Involving Divided Differences of the Di- and Tri-gamma Functions to Be Completely Monotonic
نویسنده
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.
منابع مشابه
Necessary and Sufficient Conditions for a Function Involving a Ratio of Gamma Functions to Be Logarithmically Completely Monotonic
In the paper, necessary and sufficient conditions are presented for a function involving a ratio of two gamma functions to be logarithmically completely monotonic, and some known monotonicity and inequality results are generalized and extended.
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