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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A new characterization of ultraspherical polynomials


Authors: R. Lasser and J. Obermaier
Journal: Proc. Amer. Math. Soc. 136 (2008), 2493-2498
MSC (2000): Primary 33C45; Secondary 42C05
Published electronically: March 19, 2008
MathSciNet review: 2390518
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Abstract: We characterize the class of ultraspherical polynomials in between all symmetric orthogonal polynomials on $ [-1,1]$ via the special form of the representation of the derivatives $ p'_{n+1}(x)$ by $ p_k(x),\;\;k=0,...,n.$


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Additional Information

R. Lasser
Affiliation: Helmholtz Zentrum München, German Research Center for Environmental Health, Institute of Biomathematics and Biometry, Ingolstädter Landstraße 1, 85764 Neuherberg, Germany; and Münich University of Technology, Centre of Mathematics, 85748 Garching, Germany
Email: lasser@helmholtz-muenchen.de

J. Obermaier
Affiliation: Helmholtz Zentrum München, German Research Center for Environmental Health, Institute of Biomathematics and Biometry, Ingolstädter Landstraße 1, 85764 Neuherberg, Germany
Email: josef.obermaier@helmholtz-muenchen.de

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09378-7
PII: S 0002-9939(08)09378-7
Keywords: Orthogonal polynomials, ultraspherical polynomials
Received by editor(s): March 6, 2007
Published electronically: March 19, 2008
Communicated by: Peter A. Clarkson
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.