A deformation of Hermite polynomials

2000/10/02 by M. Mekhfi, Mekhfi, M.
Mathematics · Physics and Astronomy · #33C45 #34A35 #Advanced Differential Equations and Dynamical Systems #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #math-ph #math.CA #math.FA #math.MP #msc:33C45 #msc:34A35

paper · pdf · doi:10.48550/arxiv.math-ph/0010003

16 pages, Latex

arxiv created 2000/10/02 · openalex publication_date 2000/10/02 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We propose and study the properties of a set of polynomials M_{nα, H} ^s(z), C_{nα, H}^s(z) W_{nα, H}^s(z) with n,s∈ N ;α=± 1;and where H stands for Hermite ; the ''root '' polynomial >.These polynomials are obtained from a deformation of Hermite polynomials H_n(z).The structure underlying the deformation seems quite general and not only restricted to Hermite polynomials.

Related

• The M_L(z);C_L(z);W_L(z) associated Laguerre Polynomials
• Deformed Complex Hermite Polynomials
• Generalized Hermite polynomials
• An operational point of view to the theory of multi-variable/multi-index Hermite polynomials
• A partial-sum deformation for a family of orthogonal polynomials