Even and odd functions

Remarks

The graph of an even function is symmetric about the $y$-axis. The graph of an odd function is symmetric about the origin. For example, $x^2$ and $\cos x$ are even, and $x^3$ and $\sin x$ are odd. Each function splits in a unique way into an even part and an odd part: $f(x) = \frac{f(x) + f(-x)}{2} + \frac{f(x) - f(-x)}{2}$. Leonhard Euler introduced the two notions in 1727. Mathlib defines even functions as Function.Even.