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The finite Fourier transform of classical polynomials

Abstract : The finite Fourier transform of a family of orthogonal poly-nomials An(x), is the usual transform of the polynomial extended by 0 outside their natural domain. Explicit expressions are given for the Legendre, Jacobi, Gegenbauer and Chebyshev families.
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Atul Dixit, Lin Jiu, Victor H. Moll, Christophe Vignat. The finite Fourier transform of classical polynomials. Journal of the Australian Mathematical Society, Cambridge University Press, 2015, pp.145-160. ⟨10.1017/s1446788714000500⟩. ⟨hal-01116888⟩

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