Let $f : \mathbb{R}^n \to \mathbb{R}^m$ be an D3998: Odd euclidean real function.
Let $f_{\mathsf{odd}} : \mathbb{R}^n \to \mathbb{R}^m$ be the D4693: Function odd part of $f$.

Then \begin{equation} f = f_{\mathsf{odd}} \end{equation}