Orthogonal polynomial solutions of linear ordinary differential equations

摘要

This paper surveys the latest known results concerning the classification of differential equations of the form∑k=1Nak(x)y(k)(x)=λy(x)having a sequence of polynomial eigenfunctions {pn(x)}n=0∞ that are orthogonal with respect to some real bilinear form. Since the publishing of the Erice Report in 1990, several new significant results and generalizations have been discovered.