Exceptional Hahn and Jacobi orthogonal polynomials

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• 作者：Antonio J. Dur&aacute ; n ^duran@us.es
• 关键词：42C05 ; 33C45 ; 33E30
• 刊名：Journal of Approximation Theory
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：214
• 期：Complete
• 页码：9-48
• 全文大小：514 K
• 卷排序：214

文摘

Using Casorati determinants of Hahn polynomials (hnα,β,N)n, we construct for each pair F=(F1,F2)F=(F1,F2) of finite sets of positive integers polynomials hnα,β,N;F, n∈σFn∈σF, which are eigenfunctions of a second order difference operator, where σFσF is certain set of nonnegative integers, σF⊊︀NσF⊊︀N. When N∈NN∈N and αα, ββ, NN and FF satisfy a suitable admissibility condition, we prove that the polynomials hnα,β,N;F are also orthogonal and complete with respect to a positive measure (exceptional Hahn polynomials). By passing to the limit, we transform the Casorati determinant of Hahn polynomials into a Wronskian type determinant of Jacobi polynomials (Pnα,β)n. Under suitable conditions for αα, ββ and FF, these Wronskian type determinants turn out to be exceptional Jacobi polynomials.