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

`\[f(x_{1},\ldots ,x_{n})=\sum _{\nu \in \mathbb {N} ^{n}}a_{\nu }x^{\nu }=\sum _{\nu \in \mathbb {N} ^{n}}a_{\nu }x_{1}^{\nu _{1}}x_{2}^{\nu _{2}}\cdots x_{n}^{\nu _{n}}\,\]`

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```with \(a_{\nu }\in \mathbb {R} \) and \(a_{\nu }\neq 0\) for finitely many \(a_{\nu }\).

### References

#### Adapted from CC BY-SA 3.0 Sources:

**Brenner, Prof. Dr. rer. nat., Holger**: Various courses at the University of OsnabrÃ¼ck

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