Some Inequalities About The Functions Related To Gamma Functions

The main content of this paper is the asymptotic expansions and inequalities of the Gam-ma function?Psi function?Polygamma function?incomplete Gamma function and the asympt-otic expansion and inequality of the related functions composed of these special functions.The research consists of three aspects:1.Through the inequalities by S.R.Tims and J.A.Tyrrell et al.This paper first establishes an asymptotic expansion and gets a new inequality based on this asymptotic expansion.2.This paper first establishes an asymptotic expansion aboutI_p(x)and then gets a new inequality based on the asymptotic expansion.3.In the paper,based on some inequalities of the Gamma function and its related functio-ns,the mean value theorem is mainly used to improve the inequalities of the Gamma functi-on and related functions.Including the Gamma function,the standard product of the Gamma function,the ratio of Gamma function,and the Polygamma function in the complex domain.And the better conclusions are obtained through the properties of these functions.