Some properties of analytical functional element

The article introduces the concept of analytic functional element and the analyticity of function in n-dimensional point for functions of many complex variables. Further, we describe some properties of the theory of many complex variables and consider their application in the theory of differential equations. While using the Cauchy’s integral formula, various statements and implications from them are introduced, as well as for the functions of one complex variable. The uniformly convergent series of analytic functions are used for the proof of some theorems.