Definition:Field of Formal Laurent Series

Definition
Let $k$ be a field.

The ring of formal Laurent series $k((X))$ over $k$ in a variable $X$ is also called the field of formal Laurent series.

Also denoted as
Since $k((X))$ is a field, by Variable of Ring of Formal Laurent Series is Nonzero we may assume $X = Y^{-1}$ is the multiplicative inverse of some element $Y$, and write $k((X)) = k((Y^{-1}))$.

Also see

 * Ring of Formal Laurent Series over Field is Field