 Puiseux series

A Puiseux series permits fractional exponents with a fixed common denominator: ${\sum }_{n\ge n_0}{a}_n{z}^{n/q}$. These are natural local expansions of branches of algebraic functions. A fractional-power root expansion uses such powers to resolve roots that coalesce as a parameter tends to zero.

A Puiseux series is a type of power series that allows for fractional exponents and is used in algebraic geometry and the study of singularities. It can be thought of as a generalization of the Taylor series or Laurent series.