A characterization of ultraspherical, Hermite, and Chebyshev polynomials of the first kind
Abstract
We show that the only orthogonal polynomials with a generating function of the form F(x z - α z2) 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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