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

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 $F(x w(z) - R(z))$.

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