Monotonicity properties related to the ratio of two gamma functions

TL;DR

This paper explores the monotonicity of the ratio of gamma functions, deriving new inequalities and asymptotics, and confirming existing conjectures in the mathematical analysis of gamma functions.

Contribution

It provides new monotonicity properties and inequalities for gamma function ratios, extending previous conjectures and establishing related asymptotic behaviors.

Findings

Established new monotonicity properties of gamma function ratios

Derived inequalities and asymptotic expansions related to gamma functions

Confirmed conjectures proposed by C.-P. Chen

Abstract

In this paper we investigate the monotonicity properties related to the ratio of gamma functions, from which some related asymptotics and inequalities are established. Some special cases also confirm the conjectures of C.-P. Chen [Monotonicity properties, inequalities, and asymptotic expansions associated with the gamma function. Appl. Math. Comput. 283 (2016), 385--396.].