Bounds for the ratio of two gamma functions--From Wendel's limit to Elezovi\'c-Giordano-Pe\v{c}ari\'c's theorem

Abstract

In the survey paper, along one of main lines of bounding the ratio of two gamma functions, we look back and analyse some known results, including Wendel's, Gurland's, Kazarinoff's, Gautschi's, Watson's, Chu's, Lazarevi\'c-Lupa\c{s}'s, Kershaw's and Elezovi\'c-Giordano-Pe\v{c}ari\'c's inequalities, claim, monotonic and convex properties. On the other hand, we introduce some related advances on the topic of bounding the ratio of two gamma functions in recent years.