A Note on an Open Problem

An, Miao-Qing (2009) A Note on an Open Problem. Research report collection, 12 (2).


The function (Γ(x+1)¹/x)/((x+β)α) is logarithmically completely monotonic on (0,∞) for α ≥ 1 and 0 ≤ β ≤ 1, and is logarithmically completely monotonic in (−1, 0) for 0 < α ≤ (2β)/(1+2β)� and β > 1. This gives an answer to an open problem proposed by Feng Qi.

Item type Article
URI https://vuir.vu.edu.au/id/eprint/18953
Subjects Historical > FOR Classification > 0101 Pure Mathematics
Current > Collections > Research Group in Mathematical Inequalities and Applications (RGMIA)
Keywords gamma function, psi function, polygamma function, complete monotonicity, logarithmically complete monotonicity
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