Two classes of special functions using Fourier transforms of some finite classes of classical orthogonal polynomials
Authors:
Wolfram Koepf and Mohammad MasjedJamei
Journal:
Proc. Amer. Math. Soc. 135 (2007), 35993606
MSC (2000):
Primary 33C45
Published electronically:
June 29, 2007
MathSciNet review:
2336575
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Abstract: Some orthogonal polynomial systems are mapped onto each other by the Fourier transform. The bestknown example of this type is the Hermite functions, i.e., the Hermite polynomials multiplied by , which are eigenfunctions of the Fourier transform. In this paper, we introduce two new examples of finite systems of this type and obtain their orthogonality relations. We also estimate a complicated integral and propose a conjecture for a further example of finite orthogonal sequences.
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Additional Information
Wolfram Koepf
Affiliation:
Department of Mathematics, University of Kassel, HeinrichPlettStr. 40, D34132 Kassel, Germany
Email:
koepf@mathematik.unikassel.de
Mohammad MasjedJamei
Affiliation:
Department of Mathematics, K. N. Toosi University of Technology, Sayed Khandan, Jolfa Av., Tehran, Iran
Email:
mmjamei@yahoo.com
DOI:
http://dx.doi.org/10.1090/S0002993907088892
PII:
S 00029939(07)088892
Keywords:
Classical orthogonal polynomials,
Fourier transform,
hypergeometric functions,
Gosper identity,
Ramanujan integral
Received by editor(s):
January 1, 2006
Received by editor(s) in revised form:
August 16, 2006
Published electronically:
June 29, 2007
Communicated by:
Carmen C. Chicone
Article copyright:
© Copyright 2007
American Mathematical Society
