Join the Polygon club for the second part of their series.

In 1997, Gian-Carlo Rota delivered at an MAA meeting his thoughts on undergraduate curriculum for differential equations; he expresses
(1) his reserve towards the inclusion of linear differential equations with variable coefficients, and
(2) his desire towards an inclusion of differential algebra as a topic.
He states his reason for the discouragement (1) to be the absence of explicit solutions, “(w)ith the exception of the Euler-Cauchy differential equation, ... no other second order linear differential equation can be solved explicitly, unless one introduces special functions”, and his reason for the encouragement (2) to be the availability of explicit formulas for certain algebraic constructs: “... even though there is no formula for the general solution of a second order linear differential equation, there is nevertheless an explicit formula for the Wronskian of two solutions.”

In this seminar, professor Yoon will discuss (a) D-finite series as a tool used by combinatorists to examine power series solutions to linear differential equations, (b) present an explicit formula for all D-finite series, and (c) discuss potential ideas for obtaining explicit solutions to linear ODE in general.