Different coordinate systems and periodicity

In the article we consider a two new systems of coordinate for the p,w complex variables. The centers of coordinates of the systems are located in the (0, 0), ( 𝐴, 0) points, > 0. With point of view of the centers we obtain some new equations of the (𝑝, (𝑝)) set of points for the (𝑝) function. The consideration of the equations results in periodicity of the f(p) function, if the𝑓 (𝑝) function is regular in some open G set of points. Similar theorems are proved for the irregular functions. The example of two reverse functions for a new system of coordinates is resulted. The theorem is proved about the (𝑝) = 0 equality for wide class of regular functions, if Im = 0.