**even**if and only if \begin{equation} \forall \, x \in \mathbb{R}^N : f(-x) = f(x) \end{equation}

Definition D3997

Even euclidean real function

Formulation 0

A D4363: Euclidean real function $f : \mathbb{R}^N \to \mathbb{R}^M$ is **even** if and only if
\begin{equation}
\forall \, x \in \mathbb{R}^N
: f(-x) = f(x)
\end{equation}

Children

▶ | D4696: Conjugate-even complex function |

▶ | D5480: Even real function |

Results

▶ | R4287: Finite product of even complex functions is even |

▶ | R2928: Finite sum of even euclidean real functions is even |

▶ | R2959: Function even part is even |