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

Associated Legendre transform is defined as

The inverse Legendre transform is given by

Some Legendre transform pairs

References

  1. Debnath, Lokenath; Dambaru Bhatta (2007). Integral transforms and their applications (2nd ed.). Boca Raton: Chapman & Hall/CRC. ISBN 9781482223576.
  2. Churchill, R. V. (1954). "The Operational Calculus of Legendre Transforms". Journal of Mathematics and Physics. 33 (1–4): 165–178. doi:10.1002/sapm1954331165. hdl:2027.42/113680.
  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.


This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.