A characterization of ultraspherical polynomials

Details A characterization of ultraspherical polynomials A characterization of ultraspherical polynomials

2011-08-03

arxiv.org/abs/1108.0914v1

Mathematics

Classical Analysis and ODEs

Scientific paper

This is an expository article, with all details included.
We show that the only orthogonal polynomials with a generating function of
the form $F(x z - a z^2)$ are the ultraspherical, Hermite, and Chebyshev
polynomials of the first kind. The generating function for the Chebyshev case
is non-standard, although it is easily derived from the usual one.

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