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Series Expansions of Algebraic Functions

  • Deryn Griffiths
Part of the Mathematics and Its Applications book series (MAIA, volume 325)

Abstract

Algebraic functions over Q(X) may indeed be expressed as Puiseux series. We examine an algorithm for the development of the series expansion for algebraic functions. From the algorithm we show why the series developed over fields of finite characteristic will not necessarily be Puiseux.

The series y = 1 + X 1/2 + X 3/4 + X 7/8 + ... satisfies y 2 + Xy + 1+ X = 0 over F 2. The shape of such series, which satisfy algebraic functions but which are not Puiseux series, is explored.

Keywords

Power Series Series Expansion Dirichlet Series Fractional Power Algebraic Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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Copyright information

© Springer Science+Business Media Dordrecht 1995

Authors and Affiliations

  • Deryn Griffiths
    • 1
  1. 1.School of Mathematics & StatisticsUniversity of SydneyAustralia

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