2011/05/31 by Satoru Odake, Ryu Sasaki
Mathematics · Physics and Astronomy · #Algebra over a field #Classical orthogonal polynomials #Combinatorics #Computer science #Difference polynomials #Discrete orthogonal polynomials #Gegenbauer polynomials #Hahn polynomials #Integer (computer science) #Laguerre polynomials #Mathematical analysis #Mathematics #Nonlinear Waves and Solitons #Orthogonal polynomials #Polynomial #Pure mathematics #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Wilson polynomials #hep-th #math-ph #math.CA #math.MP #nlin.SI #quant-ph
paper · pdf · doi:10.1016/j.physletb.2011.06.075
published as Phys.Lett. B702 (2011) 164-170 · 7 pages, 1 figure. Comments and references added. Typo corrected(4,5 lines below eq.(5)). To appear in Phys.Lett.B
arxiv created 2011/06/28 · openalex publication_date 2011/07/06 · arxiv updated 2015/05/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Infinite families of multi-indexed orthogonal polynomials are discovered as the solutions of exactly solvable one-dimensional quantum mechanical systems. The simplest examples, the one-indexed orthogonal polynomials, are the infinite families of the exceptional Laguerre and Jacobi polynomials of types I and II constructed by the present authors. The totality of the integer indices of the new polynomials are finite and they correspond to the degrees of the ‘virtual state wavefunctions’ which are ‘deleted’ by the generalisation of Crum–Adler theorem. Each polynomial has another integer n which counts the nodes.