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.References
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Additional Information
- Mohammad Masjed-Jamei
- Affiliation: Department of Mathematics, K. N. Toosi University of Technology, P.O. Box 16315-1618, Tehran, Iran – and – School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P. O. Box 19395-5746, Tehran, Iran
- Email: mmjamei@kntu.ac.ir, mmjamei@yahoo.com
- Wolfram Koepf
- Affiliation: Institute of Mathematics, University of Kassel, Heinrich-Plett-Str. 40, D-34132 Kassel, Germany
- Email: koepf@mathematik.uni-kassel.de
- Received by editor(s): August 17, 2010
- Received by editor(s) in revised form: January 10, 2011, and February 10, 2011
- Published electronically: October 14, 2011
- Additional Notes: This research was supported in part by a grant from IPM, No. 89330021, and by a grant from “Bonyade Mellie Nokhbegan”, No. PM/1184
- Communicated by: Walter Van Assche
- © Copyright 2011 By the authors
- Journal: Proc. Amer. Math. Soc. 140 (2012), 2053-2063
- MSC (2010): Primary 33C45, 42A38
- DOI: https://doi.org/10.1090/S0002-9939-2011-11063-3
- MathSciNet review: 2888193