Normality Concerning Higher Derivative In Meromorphic Functions

One of the important research topics in the single complex variable function is the normality of the normal family.Its value distribution of meromorphic functions,differential equations,uniqueness of meromorphic functions and dynamic systems in the complex field are of universal and far-reaching significance.Its core development object is the research of the normal family.In this paper,we mainly study the normality of meromorphic functions and holomorphic functions involving higher derivatives by using the related theoretical knowledge of normal families of meromorphic functions and improve and further generalize some previous results.The full text is divided into four parts:We firstly briefly review the research background,significance,and research content of the normal family theory;Secondly,we will give the basic theoretical knowledge needed in this paper,such as some basic concepts and some research results of normal families;Next,The normality theorem of meromorphic functions involving high-order derivative differential polynomials is studied,and the existing conclusions are extended and further improved;Finally,mainly discuss some generalizations of normal criteria and inferences where holomorphic functions are shared by every function from the family and its higher derivative are studied.