Representations of degenerate Hermite polynomials

2020/10/28 by Taekyun Kim, Kim, Taekyun, Dae San Kim +7 · 2 citations
Mathematics · Physics and Astronomy · #05A40 #11B68 #11B83 #Advanced Mathematical Identities #Algebraic structures and combinatorial models #FOS: Mathematics #Number Theory (math.NT) #Quantum Mechanics and Non-Hermitian Physics

paper · pdf · doi:10.48550/arxiv.2010.14696

openalex publication_date 2020/10/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce degenerate Hermite polynomials as a degenerate version of the ordinary Hermite polynomials. Then, among other things, by using the formula about representing one lambda-Sheffer polynomial in terms of other lambda-Sheffer polynomials we represent the degenerate Hermite polynomials in terms of the higher-order degenerate Bernoulli, Euler, and Frobenius-Euler polynomials and vice versa.

Cited by

• The Multivariable Generalized Hermite-Type-Genocchi Polynomials of Order a
• Operational-umbral approach to bivariate degenerate Hermite polynomials and their partial orthogonality

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