The finite Fourier transform of classical polynomials

Atul Dixit , Lin Jiu , Victor H. Moll , Christophe Vignat

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classification 🧮 math.FA math.CA

keywords transformfinitefourierpolynomialschebyshevclassicaldomainexplicit

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The finite Fourier transform of a family of orthogonal polynomials $A_{n}(x)$, 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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The finite Fourier transform of classical polynomials

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