publication . Article . Preprint . 2014

The finite Fourier transform of classical polynomials

Atul Dixit; Lin Jiu; Victor H. Moll; Christophe Vignat;
Open Access English
  • Published: 22 Feb 2014
  • Publisher: HAL CCSD
  • Country: France
<jats:title>Abstract</jats:title><jats:p>The finite Fourier transform of a family of orthogonal polynomials is the usual transform of these polynomials extended by<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="" mime-subtype="gif" xlink:type="simple" xlink:href="S1446788714000500_inline1" /><jats:tex-math>$0$</jats:tex-math></jats:alternatives></jats:inline-formula>outside their natural domain of orthogonality. Explicit expressions are given for the Legendre, Jacobi, Gegenbauer and Chebyshev families.</jats:p>
Persistent Identifiers
free text keywords: [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], Mathematics - Functional Analysis, Mathematics - Classical Analysis and ODEs, 42A16, 33C45, General Mathematics, Orthogonal polynomials, Pure mathematics, Chebyshev filter, Legendre polynomials, Mathematics, Expression (mathematics), Orthogonality, Polynomial, Finite fourier transform

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