Legendre transform (integral transform)
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This article is about an integral transform using Legendre polynomials. For the involution transform commonly used in classical mechanics and thermodynamics, see Legendre transformation.
In mathematics, Legendre transform is an integral transform named after the mathematician Adrien-Marie Legendre, which uses Legendre polynomials as kernels of the transform. Legendre transform is a special case of Jacobi transform.
The Legendre transform of a function is[1][2][3]
The inverse Legendre transform is given by