Affiliation:
1. Departamento de Matemática Universidade Federal do Rio de Janeiro, Campus UFRJ Duque de Caxias Prof. Geraldo Cidade Duque de Caxias Rio de Janeiro Brazil
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].
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