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arXiv · 1108.0914

A characterization of ultraspherical, Hermite, and Chebyshev polynomials of the first kind

Michael Anshelevich
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Abstract

We show that the only orthogonal polynomials with a generating function of the form $F(x z - \alpha z^2)$ are the ultraspherical, Hermite, and Chebyshev polynomials of the first kind. For special $F$ for which this is the case, we then finish the classification of orthogonal polynomials with more general generating functions $F(x w(z) - R(z))$.

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Michael Anshelevich. 2011-08-03. A characterization of ultraspherical, Hermite, and Chebyshev polynomials of the first kind. https://arxiv.org/abs/1108.0914

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