A new characterization of ultraspherical polynomials
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- by R. Lasser and J. Obermaier
- Proc. Amer. Math. Soc. 136 (2008), 2493-2498
- DOI: https://doi.org/10.1090/S0002-9939-08-09378-7
- Published electronically: March 19, 2008
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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 $p_k(x),\;\;k=0,...,n.$References
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Bibliographic 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
- Received by editor(s): March 6, 2007
- Published electronically: March 19, 2008
- Communicated by: Peter A. Clarkson
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 136 (2008), 2493-2498
- MSC (2000): Primary 33C45; Secondary 42C05
- DOI: https://doi.org/10.1090/S0002-9939-08-09378-7
- MathSciNet review: 2390518