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Hermite transform

From Wikipedia, the free encyclopedia

In mathematics, the Hermite transform is an integral transform named after the mathematician Charles Hermite that uses Hermite polynomials as kernels of the transform.

The Hermite transform of a function is

The inverse Hermite transform is given by

Some Hermite transform pairs

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[1]
[2]
[3]
[4]
[5][6]

References

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  1. ^ McCully, Joseph Courtney; Churchill, Ruel Vance (1953), Hermite and Laguerre integral transforms : preliminary report
  2. ^ Feldheim, Ervin (1938). "Quelques nouvelles relations pour les polynomes d'Hermite". Journal of the London Mathematical Society (in French). s1-13: 22–29. doi:10.1112/jlms/s1-13.1.22.
  3. ^ Bailey, W. N. (1939). "On Hermite polynomials and associated Legendre functions". Journal of the London Mathematical Society. s1-14 (4): 281–286. doi:10.1112/jlms/s1-14.4.281.
  4. ^ Glaeske, Hans-Jürgen (1983). "On a convolution structure of a generalized Hermite transformation" (PDF). Serdica Bulgariacae Mathematicae Publicationes. 9 (2): 223–229.
  5. ^ Erdélyi et al. 1955, p. 194, 10.13 (22).
  6. ^ Mehler, F. G. (1866), "Ueber die Entwicklung einer Function von beliebig vielen Variabeln nach Laplaceschen Functionen höherer Ordnung" [On the development of a function of arbitrarily many variables according to higher-order Laplace functions], Journal für die Reine und Angewandte Mathematik (in German) (66): 161–176, ISSN 0075-4102, ERAM 066.1720cj. See p. 174, eq. (18) and p. 173, eq. (13).

Sources

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