Definition:Legendre Transform

Definition
Let $\map f x$ be a strictly convex real function.

Let $p=\map {f'} x$.

Let $\map {f^*} p=-\map f{\map x p}+p\map x p$.

The Legendre Transform on $x$ and $f$ is the mapping of the variable and function pair:
 * $\paren{x,\map f x}\to\paren{p,\map {f^*} p}$