An asymptotic expansion of eigenpolynomials for a class of linear differential operators

Abstract

AbstractConsider an M‐th order linear differential operator, ,where is a monic complex polynomial such that and are complex polynomials such that . It is known that the zero counting measure of its eigenpolynomials converges in the weak star sense to a measure μ. We obtain an asymptotic expansion of the eigenpolynomials of in compact subsets out of the support of μ. In particular, we solve a conjecture posed in Masson and Shapiro [On polynomial eigenfunctions of a hypergeometric type operator. Exper Math. 2001;10:609‐618].