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



Publication Details
Authors:
Koepf, W.; Masjed-Jamei, M.
Publication year:
2012
Journal:
Proceedings of the American Mathematical Society
Pages range:
2053-2063
Volume number:
140
ISSN:
0002-9939

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.


Research Areas


Last updated on 2019-01-11 at 16:05