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

2009/04/07 by Feng Qi · 2 citations
Mathematics · #Analytic and geometric function theory #Bounding overwatch #Function (biology) #Gamma function #Inequality #Mathematical Inequalities and Applications #Mathematical functions and polynomials #Monotonic function #math.CA #msc:26A48 #msc:26A51 #msc:26D07 #msc:26D20 #msc:33B15 #msc:33D05 #msc:65R10

paper · pdf · doi:10.12691/tjant-2-5-1

published as Turkish Journal of Analysis and Number Theory 2 (2014), no. 5, 152--164 · 19 pages

arxiv created 2009/04/07 · openalex publication_date 2014/09/27 · arxiv updated 2014/11/04 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

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 <i>q-</i>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.

Cited by

• Zero Distribution of Polynomials Generated by a Power of a Cubic Polynomial
• Diffeomorphic Markov Chain Monte Carlo: fast mixing for heavy-tailed distributions

Related

• Bounds for the ratio of two gamma functions--From Wendel's and related inequalities to logarithmically completely monotonic functions
• Monotonicity properties related to the ratio of two gamma functions
• Further Inequalities Associated with the Classical Gamma Function
• Necessary and sufficient conditions for two classes of functions to be logarithmically completely monotonic
• Logarithmically Complete Monotonicity of Certain Ratios Involving the k-Gamma Function