Legendre transform (integral transform)

In mathematics, Legendre transform is an integral transform named after the mathematician Adrien-Marie Legendre, which uses Legendre polynomials

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 Associated Legendre transform is defined as The inverse Legendre transform is given by

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