Legendre transform

From Wikipedia, the free encyclopedia
Jump to navigation Jump to search

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

Associated Legendre transform[edit]

Associated Legendre transform is defined as

The inverse Legendre transform is given by

Some Legendre transform pairs[edit]


  1. ^ Debnath, Lokenath, and Dambaru Bhatta. Integral transforms and their applications. CRC press, 2014.
  2. ^ Churchill, R. V. "The operational calculus of Legendre transforms." Studies in Applied Mathematics 33.1–4 (1954): 165–178.
  3. ^ Churchill, R. V., and C. L. Dolph. "Inverse transforms of products of Legendre transforms." Proceedings of the American Mathematical Society 5.1 (1954): 93–100.