Given a function of two variables
 |  |  |
(1)
|
 |  |  |
(2)
|
change the differentials from 
and 
to 
and 
with the transformation
 |
(3)
|
 |  |  |
(4)
|
 |  |  |
(5)
|
 |  |  |
(6)
|
Then
 |  |  |
(7)
|
 |  |  |
(8)
|
Legendre Transformation
See also
Legendre TransformExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Legendre Transformation." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/LegendreTransformation.html