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

Authors: Mohammad Masjed-Jamei and Wolfram Koepf
Journal: Proc. Amer. Math. Soc. 140 (2012), 2053-2063
MSC (2010): Primary 33C45, 42A38
Posted: October 14, 2011
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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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