COMPLETELY MONOTONIC FUNCTIONS INVOLVING THE GAMMA AND q-GAMMA FUNCTIONS
نویسندگان
چکیده
We give an infinite family of functions involving the gamma function whose logarithmic derivatives are completely monotonic. Each such function gives rise to an infinitely divisible probability distribution. Other similar results are also obtained for specific combinations of the gamma and q-gamma functions.
منابع مشابه
Bounds for the Ratio of Two Gamma Functions—from Gautschi’s and Kershaw’s Inequalities to Completely Monotonic Functions
Abstract. In this expository and survey paper, along one of main lines of bounding the ratio of two gamma functions, we look back and analyse some inequalities, the complete monotonicity of several functions involving ratios of two gamma or q-gamma functions, the logarithmically complete monotonicity of a function involving the ratio of two gamma functions, some new bounds for the ratio of two ...
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