用本影代数方法研究sheffer -λ多项式

IF 1.2 4区物理与天体物理 Q3 PHYSICS, MATHEMATICAL

Reports on Mathematical Physics Pub Date : 2025-04-01 DOI:10.1016/S0034-4877(25)00025-4

UMME ZAINAB

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引用次数: 0

摘要

本文引入了sheffer相关λ多项式族，并建立了它们的拟单项式性质。此外，利用本影代数矩阵代数探讨了这些多项式的某些性质。这种方法为研究多变量特殊多项式的性质提供了一个强有力的工具。利用帕斯卡泛函和朗斯基矩阵的性质和关系，推导出这些多项式的递归公式和微分方程。并得到了相关λ多项式和apell -λ多项式族的相应结果。此外，这些发现证明了Hermite-λ，指数-λ和Miller-Lee-λ多项式。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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THE UMBRAL-ALGEBRAIC APPROACH TO STUDY THE SHEFFER-λ POLYNOMIALS

In this article, the family of Sheffer-associated λ polynomials is introduced, and their quasi-monomial properties are established. Additionally, certain properties of these polynomials are explored using umbral algebraic matrix algebra. This approach provides a powerful tool for investigating the properties of multi-variable special polynomials. The recursive formulae and differential equations for these polynomials are derived using the properties and relationships between the Pascal functional and Wronskian matrices. The corresponding results for the Appellassociated λ polynomials and Appell-λ polynomial families are also obtained. Furthermore, these findings are demonstrated for the Hermite-λ, exponential-λ, and Miller-Lee-λ polynomials.

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来源期刊

Reports on Mathematical Physics 物理-物理：数学物理

CiteScore

1.80

自引率

0.00%

发文量

审稿时长

6 months

期刊介绍： Reports on Mathematical Physics publish papers in theoretical physics which present a rigorous mathematical approach to problems of quantum and classical mechanics and field theories, relativity and gravitation, statistical physics, thermodynamics, mathematical foundations of physical theories, etc. Preferred are papers using modern methods of functional analysis, probability theory, differential geometry, algebra and mathematical logic. Papers without direct connection with physics will not be accepted. Manuscripts should be concise, but possibly complete in presentation and discussion, to be comprehensible not only for mathematicians, but also for mathematically oriented theoretical physicists. All papers should describe original work and be written in English.