Talk:Puiseux expansion

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[edit] all Puiseux series have positive radius of convergence?

I'm a little bit confused the the statement that all Puiseux series of positive radius of convergence. Surely the algebraic closure contains many series that don't converge?--345Kai (talk) 04:51, 26 November 2007 (UTC)

There are several things that should be improved.

1. As the previous commenter writes, it is not correct like it is written now. If one takes the algebraic closure of the ring K[[x]] of formal power series (like is done in the article) then one obtains the ring K\langle\langle x\rangle \rangle of formal Puiseux series. However, if one takes the algebraic closure of the ring K{{x}} of convergent power series, then one obtains the ring K\langle\{x\}\rangle of convergent Puiseux series.

2. Even though this article has a generalization to transfinite series (relatively unknown) it says nothing about a generalization to several variables (known, and very much in use).