A characterization of ultraspherical, Hermite, and Chebyshev polynomials of the first kind. Issue 4 (2nd April 2016) - Anshelevich, Michael
ABSTRACT: We show that the only orthogonal polynomials with a generating function of the form F ( x z − α 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 ) ) .