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.

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