Analytical functions of an complex variable with parameters

In this paper, we consider the analytic functions of a complex variable with small parameters generated by some operators. We study the asymptotic behavior of a function with respect to a small parameter. The problem is solved using line-level harmonic functions. The analytic domain of the function is divided by some lines into parts, and in some parts the limits (bya small parameter)exist, but in others they are infinite or do not exist