# Puiseux series

A formal series of the form

$$\sum _{n=m}^{\mathrm{\infty}}{a}_{n}{z}^{n/k}$$ |

where $m$ and $k$ are integers such that $k\ge 1$ is
is called a Puiseux series^{} or a fractional power series. Note that if $k>1$, then ${z}^{n/k}$ could be multivalued. One example of the use of such a power series^{} is the Puiseux parametrization of one-dimensional complex analytic varieties.

## References

- 1 E. M. Chirka. . Kluwer Academic Publishers, Dordrecht, The Netherlands, 1989.
- 2 Alexandru Dimca. . Vieweg, Braunschweig, Germany, 1987.

Title | Puiseux series |
---|---|

Canonical name | PuiseuxSeries |

Date of creation | 2013-03-22 15:20:28 |

Last modified on | 2013-03-22 15:20:28 |

Owner | jirka (4157) |

Last modified by | jirka (4157) |

Numerical id | 5 |

Author | jirka (4157) |

Entry type | Definition |

Classification | msc 32B10 |

Synonym | fractional power series |

Related topic | PuiseuxParametrization |

Related topic | GeneralPower |