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What is Bounds for the ratio of two gamma functions--From Gautschi's and Kershaw's inequalities to completely monotonic functions about?

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 gamma functions and divided differences of polygamma functions, and related monotonicity results.

Author

Qi, Feng

Published

2009

Language

EN