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Operations on Generalized Power Series
Author(s) -
Zyczkowski Michal
Publication year - 1965
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19650450409
Subject(s) - series (stratigraphy) , generalization , power series , algebraic number , mathematics , mean reversion , variable (mathematics) , perturbation (astronomy) , computer science , calculus (dental) , algebra over a field , pure mathematics , mathematical analysis , econometrics , medicine , paleontology , physics , dentistry , quantum mechanics , biology
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.