2015/06/24 by Constanze Liaw, John Osborn · 3 citations
Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Classical orthogonal polynomials #Discrete orthogonal polynomials #Eigenfunction #Hahn polynomials #Jacobi polynomials #Laguerre polynomials #Mathematical functions and polynomials #Mehler–Heine formula #Orthogonal polynomials #Quantum Mechanics and Non-Hermitian Physics #Wilson polynomials #math.CA #math.SP #msc:33C45 #msc:34B24 #msc:42C05 #msc:44A60
paper · pdf · doi:10.1002/mana.201500250
published in Mathematische Nachrichten 290(11-12), 1716-1731 (Wiley) · 19 pages
arxiv created 2015/06/24 · openalex created_date 2016/06/24 · openalex publication_date 2017/01/04 · arxiv updated 2017/10/10 · openalex updated_date 2026/08/05
Exceptional orthogonal Laguerre polynomials can be viewed as an extension of the classical Laguerre polynomials per excluding polynomials of certain order(s) from being eigenfunctions for the corresponding exceptional differential operator. We are interested in the (so‐called) Type I X 1 ‐Laguerre polynomial sequence , and , where the constant polynomial is omitted. We derive two representations for the polynomials in terms of moments by using determinants. The first representation in terms of the canonical moments is rather cumbersome. We introduce adjusted moments and find a second, more elegant formula. We deduce a recursion formula for the moments and the adjusted ones. The adjusted moments are also expressed via a generating function. We observe a certain detachedness of the first two moments from the others.