Hermite transform
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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
[1] | |
[2] | |
[3] | |
[4] | |
[5][6] | |
References
- ↑ McCully, Joseph Courtney; Churchill, Ruel Vance (1953), Hermite and Laguerre integral transforms : preliminary report
- ↑ Feldheim, Ervin (1938). "Quelques nouvelles relations pour les polynomes d'Hermite". Journal of the London Mathematical Society (in français). s1-13: 22–29. doi:10.1112/jlms/s1-13.1.22.
- ↑ 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.
- ↑ Glaeske, Hans-Jürgen (1983). "On a convolution structure of a generalized Hermite transformation" (PDF). Serdica Bulgariacae Mathematicae Publicationes. 9 (2): 223–229.
- ↑ Erdélyi et al. 1955, p. 194, 10.13 (22).
- ↑ 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 Deutsch) (66): 161–176, ISSN 0075-4102, ERAM 066.1720cj. See p. 174, eq. (18) and p. 173, eq. (13).
Sources
- Erdélyi, Arthur; Magnus, Wilhelm; Oberhettinger, Fritz; Tricomi, Francesco G. (1955), Higher transcendental functions (PDF), vol. II, McGraw-Hill, ISBN 978-0-07-019546-2, archived from the original (PDF) on 2011-07-14, retrieved 2023-11-09
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