The finite Fourier transform of classical polynomials

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Dixit , Atul; Jiu , Lin; Moll , Victor H.; Vignat , Christophe;
  • Publisher: HAL CCSD
  • Subject: [ MATH.MATH-PR ] Mathematics [math]/Probability [math.PR] | [MATH.MATH-PR]Mathematics [math]/Probability [math.PR] | Mathematics - Classical Analysis and ODEs | 42A16, 33C45 | Mathematics - Functional Analysis

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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