2012 | OriginalPaper | Chapter
Formal Power Series in One Indeterminate
Authors : Andrea Bonfiglioli, Roberta Fulci
Published in: Topics in Noncommutative Algebra
Publisher: Springer Berlin Heidelberg
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THE aim of this chapter is to collect some prerequisites on formal power series in one indeterminate, needed in this Book. One of the main aims is to furnish a purely algebraic proof of the fact that, by substituting into each other – in any order – the two series $$\sum^\infty_{n=1} \frac{x^n}{n!} \quad {\rm and} \quad \sum^\infty_{n=1} \frac{(-1)^{(n+1)}x^n}{n}$$ one obtains the result x.