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Let \(n \in \mathbb{N}\). An element \(\alpha\in \mathbb{N}^n\) is called multi-index. We write for \(\alpha\in \mathbb{N}^n\) and \(x\in \mathbb{C}^n\)

1. \(|\alpha|=\sum_{i=1}^{n} \alpha\)
2. \(\alpha! = \prod_{i=1}^{n} \alpha_i!\)
3. \(x^{\alpha}=\prod_{i=1}^{n} x_i^{\alpha_i}\)

See also Link to heading

• \(x^{\alpha}\)-estimate
• binary operations
• \(\partial^{\alpha}\)-derivative
• increasing multi-index