Two classes of special functions using Fourier transforms of generalized ultraspherical and generalized Hermite polynomials

Masjed-Jamei, Mohammad; Koepf, Wolfram

doi:10.1090/S0002-9939-2011-11063-3

Two classes of special functions using Fourier transforms of generalized ultraspherical and generalized Hermite polynomials
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by Mohammad Masjed-Jamei and Wolfram Koepf PDF

Proc. Amer. Math. Soc. 140 (2012), 2053-2063

Abstract:

Some orthogonal polynomial systems are mapped onto each other by the Fourier transform. Motivated by the paper [H. T. Koelink, On Jacobi and continuous Hahn polynomials, Proc. Amer. Math. Soc., 124 (1996) 887-898], in this paper we introduce two new classes of orthogonal functions, which are respectively Fourier transforms of the generalized ultraspherical polynomials and generalized Hermite polynomials, and then obtain their orthogonality relations using Parseval’s identity.

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