A characterization of ultraspherical, Hermite, and Chebyshev polynomials   of the first kind
  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 $F(x w(z) - R(z))$. 
Michael Anshelevich
math.CA math.CO