BYU

Abstract by Daniel South

Personal Infomation


Presenter's Name

Daniel South

Degree Level

Undergraduate

Abstract Infomation


Department

Mathematics

Faculty Advisor

Michael Griffin

Title

Jensen Polynomials for Holomorphic Functions

Abstract

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.