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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
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Abstract:
We characterize the class of ultraspherical polynomials in between all symmetric orthogonal polynomials on ![$ [-1,1]$](/proc/2008-136-07/S0002-9939-08-09378-7/gif-abstract0/img1.gif) via the special form of the representation of the derivatives  by 
References:
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- 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)
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- 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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