On a generalization of the laurent expansion theorem

Abstract

Based on the properties of the non-univalent conformal mapping ez = s a causal connection has been established between the Laurent expansion theorem and the Fourier trigonometric series expansion of functions. This connection combined with two highly significant results proved in the form of lemmas is a foundation stone of the theory. The main result is in the form of a theorem that is a natural generalization of the Laurent expansion theorem. The paper ends with a few examples that illustrate the theory.