A generalization of a polynomial of one variable is a polynomial function.
\[f\colon\cases{ \mathbb {R} ^{n}\longrightarrow \mathbb {R} ,\(x_{1},\ldots ,x_{n})\longmapsto f(x_{1},\ldots ,x_{n}),}]`
which can be written as a sum
\[f(x_{1},\ldots ,x_{n})=\sum _{\nu \in \mathbb {N} ^{n}}a_{\nu }x^{\nu }=\sum _{\nu \in \mathbb {N} ^{n}}a_{\nu }x_{1}^{\nu _{1}}x_{2}^{\nu _{2}}\cdots x_{n}^{\nu _{n}}\,\]
with \(a_{\nu }\in \mathbb {R} \) and \(a_{\nu }\neq 0\) for finitely many \(a_{\nu }\).
