Hermite transform

In mathematics, Hermite transform is an integral transform named after the mathematician Charles Hermite, which uses Hermite polynomials as kernels of the transform. This was first introduced by Lokenath Debnath in 1964.[1][2][3][4]

The Hermite transform of a function is

The inverse Hermite transform is given by

Some Hermite transform pairs

[5]
[6]
[7]

References

  1. Debnath, L. (1964). "On Hermite transform". Matematički Vesnik. 1 (30): 285–292.
  2. Debnath; Lokenath; Bhatta, Dambaru (2014). Integral transforms and their applications. CRC Press. ISBN 9781482223576.
  3. Debnath, L. (1968). "Some operational properties of Hermite transform". Matematički Vesnik. 5 (43): 29–36.
  4. Dimovski, I. H.; Kalla, S. L. (1988). "Convolution for Hermite transforms". Math. Japonica. 33: 345–351.
  5. Glaeske, Hans-Jürgen (1983). "On a convolution structure of a generalized Hermite transformation" (PDF). Serdica Bulgariacae Mathematicae Publicationes. 9 (2): 223–229.
  6. Bailey, W. N. (1939). "On Hermite polynomials and associated Legendre functions". Journal of the London Mathematical Society (4): 281–286. doi:10.1112/jlms/s1-14.4.281.
  7. Feldheim, Ervin (1938). "Quelques nouvelles relations pour les polynomes d'Hermite". Journal of the London Mathematical Society (in French): 22–29. doi:10.1112/jlms/s1-13.1.22.
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