Two classes of special functions using Fourier transforms of generalized ultraspherical and generalized Hermite polynomials
Authors:
Mohammad MasjedJamei and Wolfram Koepf
Journal:
Proc. Amer. Math. Soc. 140 (2012), 20532063
MSC (2010):
Primary 33C45, 42A38
Published electronically:
October 14, 2011
MathSciNet review:
2888193
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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) 887898], 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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Additional Information
Mohammad MasjedJamei
Affiliation:
Department of Mathematics, K. N. Toosi University of Technology, P.O. Box 163151618, Tehran, Iran – and – School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P. O. Box 193955746, Tehran, Iran
Email:
mmjamei@kntu.ac.ir, mmjamei@yahoo.com
Wolfram Koepf
Affiliation:
Institute of Mathematics, University of Kassel, HeinrichPlettStr. 40, D34132 Kassel, Germany
Email:
koepf@mathematik.unikassel.de
DOI:
http://dx.doi.org/10.1090/S000299392011110633
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
Article copyright:
© Copyright 2011
By the authors
