0x66a8cdce

\[ \newcommand{\d}{\mathrm{d}} \newcommand{\e}{\mathrm{e}} \newcommand{\i}{\mathrm{i}} \]

Let \(f\colon \mathbb{R}^n\to \mathbb{R}\) be smooth enough. Then for a multi-index \(\alpha\in \mathbb{N}^n\) we define

\begin{equation*} \partial^{\alpha}f=\partial^{\alpha_1}_1\cdots \partial_n^{\alpha_n}f. \end{equation*}

Many other notations like \(D^\alpha\) or \(\partial_{\alpha}\) are possible.