# Puiseux series

A formal series of the form

 $\sum_{n=m}^{\infty}a_{n}z^{n/k}$

where $m$ and $k$ are integers such that $k\geq 1$ is is called a 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 PuiseuxSeries 2013-03-22 15:20:28 2013-03-22 15:20:28 jirka (4157) jirka (4157) 5 jirka (4157) Definition msc 32B10 fractional power series PuiseuxParametrization GeneralPower