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Laguerre transform

From Wikipedia, the free encyclopedia

In mathematics, Laguerre transform is an integral transform named after the mathematician Edmond Laguerre, which uses generalized Laguerre polynomials as kernels of the transform.[1][2][3][4]

The Laguerre transform of a function is

The inverse Laguerre transform is given by

Some Laguerre transform pairs

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[5]
[6]

References

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  1. ^ Debnath, Lokenath, and Dambaru Bhatta. Integral transforms and their applications. CRC press, 2014.
  2. ^ Debnath, L. "On Laguerre transform." Bull. Calcutta Math. Soc 52 (1960): 69-77.
  3. ^ Debnath, L. "Application of Laguerre Transform on heat conduction problem." Annali dell’Università di Ferrara 10.1 (1961): 17-19.
  4. ^ McCully, Joseph. "The Laguerre transform." SIAM Review 2.3 (1960): 185-191.
  5. ^ Howell, W. T. "CI. A definite integral for legendre functions." The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 25.172 (1938): 1113-1115.
  6. ^ Debnath, L. "On Faltung theorem of Laguerre transform." Studia Univ. Babes-Bolyai, Ser. Phys 2 (1969): 41-45.