The domains of convergence of the degree series of variable of the complex numbers

This research considers two traditional important questions, which are interesting, at least to most mathematicians. The first question arises in the theory of the degree series of variable of the complex numbers, which concerns the relationship, if any, and their the domains of convergence. The second question arises in the theory of the degree series of several variables of the complex numbers. In this research we introduce double series and we give the definition of their convergence and divergence.