Title: Explicit evaluations of the polynomial solutions of differential equations with polynomial coefficients                                   

Speakers: Five undergraduate students (Andrew, Keegan, Kyle, Nikita and Patrick, each will take a part in the presentation)

Wednesday, March 23, 2016,  3-4 pm

Where: AVC 287N

Abstract: Second order linear differential equations with polynomial coefficients arise in many fields of physics and engineering. For example the Hermite, Legendre, and Laguerre equations are all discussed during any introductory study of quantum mechanics. It is well known that these equations possess polynomial solutions, which are a requirement for states that are bounded and physically realizable. The conditions under which more general equations possess polynomial solutions have been the subject of extensive study in recent years. In the present work, differential equations with polynomial coefficients of arbitrary degree are considered. A power series method is employed to obtain a general recurrence relation which generates polynomial solutions and the conditions for the existence of such solutions. In addition to presenting a Mathematica algorithm developed to find these polynomial solutions, some applications of where this method may be employed are discussed.