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Complete monotonicity of some specific functions. (Chinese. English summary) Zbl 1340.33003

Summary: The classical Euler gamma function is one of the most important special functions and has many extensive applications in many branches, for examples, statistics, physics, engineering and so on. The complete monotonicity plays a central role in studying the special functions. In this paper, some complete monotonicity and logarithmically complete monotonicity of some functions involving gamma functions are proved and some sufficient and necessary conditions for some special functions to be completely monotonic or logarithmically completely monotonic are proposed.

MSC:

33B15 Gamma, beta and polygamma functions
26A48 Monotonic functions, generalizations
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