Operations on Generalized Power Series
Michał Życzkowski · ZAMM ‐ Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik · 1965
Abstract The paper gives general formulae for various important operations on generalized power series of one variable (1.1). They appear often in applications (e.g. perturbation method, solution of algebraic equations). Particular attention is paid to composite operations, such as substitution, reversion and deparametrization. The formulae for reversion constitute a generalization of those given by Van Orstrand. The problem of convergency of the series is not dealt with, but the paper is devoted to computational technique and contains some examples of application.