Exceptional Hahn and Jacobi orthogonal polynomials

JOURNAL OF APPROXIMATION THEORY

卷:214

Article

Duran, Antonio J.¹ 

[1] Univ Seville, Dept Anal Matemat, Apdo POB 1160, E-41080 Seville, Spain

关键词: Orthogonal polynomials;    Exceptional polynomial;    Difference and differential operators;    Hahn polynomials;    Jacobi polynomials;   

DOI  :  10.1016/j.jat.2016.11.003

来源: Elsevier

【 摘 要 】

Using Casorati determinants of Hahn polynomials (h(n)(alpha,beta,N))n, we construct for each pair F = (F-1, F-2) of finite sets of positive integers polynomials h(n)(alpha,beta,N;F), n is an element of sigma(F) which are eigenfunctions of a second order difference operator, where IF is certain set of nonnegative integers, sigma(F) not subset of N. When N is an element of N and alpha, beta, N and F satisfy a suitable admissibility condition, we prove that the polynomials h(n)(alpha,beta,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 (P-n(alpha,beta))(n). Under suitable conditions for alpha, beta and F, these Wronskian type determinants turn out to be exceptional Jacobi polynomials. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free