Ladder operators and differential equations for orthogonal polynomials

1997/11/21 by Yang Chen, Mourad E. H. Ismail, Mourad E H Ismail · 8 citations
Mathematics · #Algebraic structures and combinatorial models #Mathematical functions and polynomials #Random Matrices and Applications

paper · doi:10.1088/0305-4470/30/22/020

openalex publication_date 1997/11/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/02

Abstract

Under some integrability conditions we derive raising and lowering differential recurrence relations for polynomials orthogonal with respect to a weight function supported in the real line. We also derive a second-order differential equation satisfied by these polynomials. We discuss the Lie algebra generated by the generalized creation and annihilation operators. From the differential equations, Plancherel - Rotach type asymptotics are derived. Under certain conditions, stated in the text, an Airy function emerges.

Citations

• A differential equation for orthogonal polynomials

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