An Etymological Dictionary of Astronomy and Astrophysics

A mathematical operation that transforms one function into another. Two differentiable functions f and g are said to be Legendre transforms of each other if their first derivatives are inverse functions of each other: df(x)/dx = (dg(x)/dx)^-1. The functions f and g are said to be related by a Legendre transformation.

See also: → Legendre equation; → transformation.