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M. Abramowitz and I. A. Stegun (Eds), Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, National Bureau of Standards, Applied Mathematics Series 55, 9th printing, Washington, 1970.

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Bounds for the Ratio of Two Gamma Functions: from Gautschi’s and Kershaw’s Inequalities to Complete Monotonicity

1Institute of Mathematics, Henan Polytechnic University, Jiaozuo City, Henan Province, China


Turkish Journal of Analysis and Number Theory. 2014, Vol. 2 No. 5, 152-164
DOI: 10.12691/tjant-2-5-1
Copyright © 2014 Science and Education Publishing

Cite this paper:
Feng Qi. Bounds for the Ratio of Two Gamma Functions: from Gautschi’s and Kershaw’s Inequalities to Complete Monotonicity. Turkish Journal of Analysis and Number Theory. 2014; 2(5):152-164. doi: 10.12691/tjant-2-5-1.

Correspondence to: Feng  Qi, Institute of Mathematics, Henan Polytechnic University, Jiaozuo City, Henan Province, China. Email: qifeng618@gmail.com, qifeng618@hotmail.com, qifeng618@qq.com

Abstract

In the expository and survey paper, along one of main lines of bounding the ratio of two gamma functions, the author looks back and analyses 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.

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