The Proximate Order And Proximate Type Of Entire Functions、Analytic Functions And Their Applications In Complex Linear Differential Equations

In this paper,the author first investigate the proximate order and proximate type of fl(2)+f2(2)when f1(z)and f1(z)are entire functions or analytic functions in the unit disc,and also study the growth of solutions of second order complex linear differential equations with coefficients having proximate order by taking advantage of Nevenlinna theory and complex oscillation theory.The thesis is divided into three chapters.In chapter 1,the author introduce some basic definitions and notations about,meromorphic function and value distribution theory.In chapter 2,the author study the proximate order and proximate type of f1(z)+f2(z)when the proximate order and proximate type of entire functions or analytic functions f1(z)+f2(z)have the same limit and the results that the author obtain improve some previous results.In chapter 3,the author apply the proximate order and proximate type of entire function or analytic function into complex linear differential equations and investigate the growth of solutions of second order linear differential equations with coefficients having proximate order,the results that obtained enrich and im-prove some previous results in complex oscillation theory.