Asymptotic analysis of generalized Hermite polynomials

2006/06/14 by Diego Dominici, Dominici, Diego
Mathematics · Physics and Astronomy · #33C45 (Primary) 34E05 #34E20 (Secondary) #Advanced Mathematical Theories and Applications #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #math.CA #msc:33C45 #msc:34E05 #msc:34E20

paper · pdf · doi:10.48550/arxiv.math/0606324

28 pages, 6 figures

arxiv created 2006/06/14 · openalex publication_date 2006/06/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We analyze the polynomials H_n^r(x) considered by Gould and Hopper, which generalize the classical Hermite polynomials. We present the main properties of H_n^r(x) and derive asymptotic approximations for large values of n from their differential-difference equation, using a discrete ray method. We give numerical examples showing the accuracy of our formulas.

Related

• Asymptotic analysis of the Hermite polynomials from their differential-difference equation
• Asymptotic analysis of the Askey-scheme II: from Charlier to Hermite
• Asymptotics for a generalization of Hermite polynomials
• Application of the method of Bonan-Clark to the generalized Hermite polynomials
• Some new asymptotic properties for the zeros of Jacobi, Laguerre and\n Hermite polynomials