Bounds for the ratio of two gamma functions--From Wendel's and related inequalities to logarithmically completely monotonic functions

Details Bounds for the ratio of two gamma functions--From Wendel's and related inequalities to logarithmically completely monotonic functions Bounds for the ratio of two gamma functions--From Wendel's and related inequalities to logarithmically completely monotonic functions

2009-04-07

arxiv.org/abs/0904.1048v1

Mathematics

Classical Analysis and ODEs

22 pages

Scientific paper

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, several complete monotonicity of functions involving ratios of two gamma or $q$-gamma functions, and necessary and sufficient conditions for functions involving ratios of two gamma or $q$-gamma functions to be logarithmically completely monotonic.

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