The power series are argued by the Cauchy formula interpreted as an orthogonal concept through the Fourier series, there is no direct expansion theorem similar to the one known for orthogonal functions. In this work we argue the power series expansons with a new method; from the position of orthogonal differential operators, which, unlike the classic one that requires knowledge of the analytical character at a point, uses said behavior in the positive semiaxis  and derive every series as a differential transformation of a single function, giving meaning to the idea of ​​origin of the series. In short, every function is the result of the action of an operator expressed as an orthogonal series of the differentiation operator acting on a basic function, the coefficients of development are expressed as integrals similar to the classic orthogonal ones. These facts allow us to formulate the concept of orthogonal operational space in analogy with the Hilbert space. In addition, we deduce the Laplace inverse in two versions for analytical functions, one already known integral and the other in terms of differential operators.