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1 results

  • THE FINITE FOURIER TRANSFORM OF CLASSICAL POLYNOMIALS
  • ATUL DIXIT, LIN JIU, VICTOR H. MOLL, CHRISTOPHE VIGNAT
  • Journal: Journal of the Australian Mathematical Society / Volume 98 / Issue 2 / April 2015
  • Published online by Cambridge University Press: 04 December 2014, pp. 145-160
  • Print publication: April 2015
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    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.