Several Asymptotic Expansions And Inequalities Related To Gamma Functions

In this paper,we mainly study the asymptotic expansion and inequality problems related to Gamma function,Psi function and Polygamma function.The main results are as follows:1.In 2016,Wang[22]proposed a generalized approximation of Gamma function in section 2 of chapter 2,a new proof method is given for the asymptotic expansion of this for-mula.By introducing the error sequence,the best constant and two-sided inequalities of Gam-ma function are obtained from the convergence rate of the sequence.In section 3,we discuss the integral form of this formula and draw several conclusions.In 2017,Lu Dawei[29]propose-d that the Burnside formula of Gamma function has the following approximation formula:In section 4,Theorem 2.4 generalizes this approximation formula into a fully asymptotic expa-nsion.2.In Chapter 3,we propose a continuous fractional approximation of Gosper formula for Gamma function The best constantai(i=1,2,3,...)and two-sided inequalities for Gamma function are determine-d according to the convergence rate of the sequence.3.In Chapter 4,we establish an asymptotic formula of Gamma function based on Tri-gam ma function,and discuss its best constant,asymptotic expansion and two-sided inequalities about Gamma function.