Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

A new characterization of ultraspherical polynomials

Author(s): R. Lasser; J. Obermaier
Journal: Proc. Amer. Math. Soc. 136 (2008), 2493-2498.
MSC (2000): Primary 33C45; Secondary 42C05
Posted: March 19, 2008
MathSciNet review: 2390518
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Abstract | References | Similar articles | Additional information

Abstract: We characterize the class of ultraspherical polynomials in between all symmetric orthogonal polynomials on via the special form of the representation of the derivatives $p'_{n+1}(x)$ by $p_k(x),\;\;k=0,...,n.$

References:

1.: W.A. Al-Salam, Characterization theorems for orthogonal polynomials, in: P. Nevai (Ed.), Orthogonal Polynomials, 1-24, NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., 294, Kluwer Acad. Publ., Dordrecht, 1990. MR 1100286 (92g:42011)
2.: T.S. Chihara, An Introduction to Orthogonal Polynomials, Gordon and Breach, New York, 1978. MR 0481884 (58:1979)
3.: M.E.H. Ismail, Classical and Quantum Orthogonal Polynomials in One Variable, Cambridge University Press, Cambridge, 2005. MR 2191786 (2007f:33001)
4.: R. Lasser, Orthogonal polynomials and hypergroups II - The symmetric case, Trans. Amer. Math. Soc. 341 (1994), 749-770. MR 1139495 (94d:33005)
5.: G. Szegö, Orthogonal Polynomials, Amer. Math. Soc., Providence, RI, 1959. MR 0106295 (21:5029)

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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: 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
Posted: March 19, 2008
Communicated by: Peter A. Clarkson
Copyright of article: Copyright 2008, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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