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THE FINITE FOURIER TRANSFORM OF CLASSICAL POLYNOMIALS

Published online by Cambridge University Press:  04 December 2014

ATUL DIXIT
Affiliation:
Department of Mathematics, Tulane University, New Orleans, LA 70118, USA email adixit@tulane.edu
LIN JIU
Affiliation:
Department of Mathematics, Tulane University, New Orleans, LA 70118, USA email ljiu@tulane.edu
VICTOR H. MOLL
Affiliation:
Department of Mathematics, Tulane University, New Orleans, LA 70118, USA email vhm@tulane.edu
CHRISTOPHE VIGNAT
Affiliation:
Department of Mathematics, Tulane University, New Orleans, LA 70118, USA email cvignat@math.tulane.edu LSS-Supelec, Universit’e Orsay Paris Sud 11, France
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Abstract

The finite Fourier transform of a family of orthogonal polynomials is the usual transform of these polynomials extended by $0$ outside their natural domain of orthogonality. Explicit expressions are given for the Legendre, Jacobi, Gegenbauer and Chebyshev families.

Type
Research Article
Copyright
Copyright © 2014 Australian Mathematical Publishing Association Inc. 

References

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