Complete monotonicity for a ratio of finitely many gamma functions

Abstract

Abstract In this paper, we solve the question completely raised by Feng Qi and Dongkyu Lim in paper “Monotonicity properties for a ratio of finite many gamma functions” published in Advances in Difference Equations and get some properties about ratios of finitely many gamma functions such as complete monotonicity, logarithmically complete monotonicity, the Bernstein function property, null point and extreme value.