Formal Power Series in One Indeterminate

  • Andrea BonfiglioliEmail author
  • Roberta Fulci
Part of the Lecture Notes in Mathematics book series (LNM, volume 2034)


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.


Associative Algebra Formal Power Series Recursion Formula Bernoulli Number Left Inverse 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of BolognaBolognaItaly

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