PlanetMath: Puiseux series

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Puiseux series

(Definition)

A formal series of the form

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

where

and

are integers such that $k \geq 1$ is is called a Puiseux series or a fractional power series. Note that if

, 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.

Bibliography

1: E. M. Chirka. Complex Analytic Sets. Kluwer Academic Publishers, Dordrecht, The Netherlands, 1989.
2: Alexandru Dimca. Topics on Real and Complex Singularities. Vieweg, Braunschweig, Germany, 1987.

"Puiseux series" is owned by jirka.

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Other names:

fractional power series

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Cross-references: complex analytic varieties, Puiseux parametrization, power series, multivalued, integers, series
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This is version 2 of Puiseux series, born on 2005-06-16, modified 2005-06-17.
Object id is 7161, canonical name is PuiseuxSeries.
Accessed 6319 times total.

Classification:

32B10 (Several complex variables and analytic spaces :: Local analytic geometry :: Germs of analytic sets, local parametrization)

Pending Errata and Addenda

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