Bounds for the ratio of two gamma functions: from Wendel’s asymptotic relation to Elezović-Giordano-Pečarić’s theorem

Journal of inequalities and applications

Feng Qi¹ 

关键词: bound;    inequality;    ratio of two gamma functions;    divided difference;    psi function;    polygamma function;    completely monotonic function;    Wallis’ formula;    inequality for sums;   

DOI  :  10.1186/1029-242X-2013-542

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In the expository review and survey paper dealing with bounds for the ratio of two gamma functions, along one of the main lines of bounding the ratio of two gamma functions, the authors look back and analyze some known results, including Wendel’s asymptotic relation, Gurland’s, Kazarinoff’s, Gautschi’s, Watson’s, Chu’s, Kershaw’s, and Elezović-Giordano-Pečarić’s inequalities, Lazarević-Lupaş’s claim, and other monotonic and convex properties. On the other hand, the authors introduce some related advances on the topic of bounding the ratio of two gamma functions in recent years. MSC: 33B15, 26A48, 26A51, 26D07, 26D15, 44A10.

【 授权许可】

CC BY