doiSerbia

Some logarithmically completely monotonic functions and inequalities for multinomial coefficients and multivariate beta functions

Qi Feng (School of Mathematical Sciences, Tianjin Polytechnic University Tianjin, China + College of Mathematics and Physics Inner Mongolia University for Nationalities Tongliao Inner Mongolia, China), qifeng618@gmail.com
Niu Da-Wei (Department of Science Henan University of Animal Husbandry and Economy Zhengzhou, Henan, China), nnddww@gmail.com
Lim Dongkyu (Department of Mathematics Education Andong National University, Andong, Republic of Korea), dgrim84@gmail.com
Guo Bai-Ni (School of Mathematics and Informatics Henan Polytechnic University Jiaozuo, Henan, China), bai.ni.guo@gmail.com

In the paper, the authors extend a function arising from the Bernoulli trials in probability and involving the gamma function to its largest ranges, find logarithmically complete monotonicity of these extended functions, and, in light of logarithmically complete monotonicity of these extended functions, derive some inequalities for multinomial coefficients and multivariate beta functions. These results recover, extend, and generalize some known conclusions.

Keywords: logarithmically complete monotonicity, completely monotonic function, gamma function, inequality, multinomial coefficient, multivariate beta function, Bernoulli trial, binomial probability