Abstract by Daniel South
Jensen Polynomials for Holomorphic Functions
Jensen polynomials are constructed from sequences of real numbers. Such polynomials arising from the Taylor coefficients of a function approximate the behavior of that function and its derivatives. We generalize recent results about the limiting behavior of Jensen polynomials whose coefficients have polynomial and exponential growth. We show that, under a suitable linear change of variable, these polynomials converge to just a few types of polynomials, including the Hermite polynomials and other families of polynomials satisfying similarly simple definitions.