Abstract: 
Formal Puiseux series are generalisations of formal power
series and formal Laurent series that also allow for fractional
exponents. They have the following general form: \[\sum_{i=N}^\infty
a_{i/d} X^{i/d}\] where N is an integer and
d is a positive integer. This
entry defines these series including their basic algebraic properties.
Furthermore, it proves the Newtonâ€“Puiseux Theorem, namely that the
Puiseux series over an algebraically closed field of characteristic 0
are also algebraically closed. 
BibTeX: 
@article{Formal_Puiseux_SeriesAFP,
author = {Manuel Eberl},
title = {Formal Puiseux Series},
journal = {Archive of Formal Proofs},
month = feb,
year = 2021,
note = {\url{https://isaafp.org/entries/Formal_Puiseux_Series.html},
Formal proof development},
ISSN = {2150914x},
}
