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

2011/08/03 by Anshelevich, Michael
#46L54 #Classical Analysis and ODEs (math.CA) #Combinatorics (math.CO) #FOS: Mathematics #Primary 33C45 #Secondary 42C05

paper · doi:10.48550/arxiv.1108.0914

Abstract

We show that the only orthogonal polynomials with a generating function of the form F(x z - αz²) 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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