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Springer Verlag, Science China Mathematics, 11(56), p. 2315-2325
DOI: 10.1007/s11425-012-4562-0
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Complete monotonicity of a function involving the divided difference of digamma functions
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Abstract
In the paper, necessary and sufficient conditions are provided for a function involving the divided difference of two psi functions to be completely monotonic. Consequently, a class of inequalities for sums are presented, the logarithmically complete monotonicity of a function involving the ratio of two gamma functions are derived, and two double inequalities for bounding the ratio of two gamma functions are discovered.