2013/10/17 by Antonio J. Duran, Antonio J. Durán, Duran, Antonio J. · 2 citations
Mathematics · Physics and Astronomy · #33C45 #33E30 #42C05 #Advanced Mathematical Identities #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical functions and polynomials #Quantum Mechanics and Non-Hermitian Physics #math.CA #msc:33C45 #msc:33E30 #msc:42C05
paper · pdf · doi:10.48550/arxiv.1310.4658
arXiv admin note: substantial text overlap with arXiv:1309.1175
arxiv created 2013/10/17 · openalex publication_date 2013/10/17 · arxiv updated 2013/10/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Using Casorati determinants of Meixner polynomials (mna,c)n, we construct for each pair \F=(F1,F2) of finite sets of positive integers a sequence of polynomials mna,c;\F, n∈ σ_\F, which are eigenfunctions of a second order difference operator, where σ_\F is certain infinite set of nonnegative integers, σ_\F \varsubsetneq \NN. When c and \F satisfy a suitable admissibility condition, we prove that the polynomials mna,c;\F, n∈ σ_\F, are actually exceptional Meixner polynomials; that is, in addition, they are orthogonal and complete with respect to a positive measure. By passing to the limit, we transform the Casorati determinant of Meixner polynomials into a Wronskian type determinant of Laguerre polynomials (Lnα)n. Under the admissibility conditions for \F and α, these Wronskian type determinants turn out to be exceptional Laguerre polynomials.