Some properties of degenerate Sheffer sequences based on algebraic approach

Mumtaz Riyasat (), Mehnaz Haneef () and Subuhi Khan ()
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Mumtaz Riyasat: Aligarh Muslim University
Mehnaz Haneef: Aligarh Muslim University
Subuhi Khan: Aligarh Muslim University

Indian Journal of Pure and Applied Mathematics, 2025, vol. 56, issue 1, 414-431

Abstract: Abstract The algebraic approach endeavor a dominant tool for investigating properties of special polynomials. The main objective of this paper is to survey briefly the properties and applications of the degenerate Sheffer sequences and corresponding hybrid forms via determinants. In this article, a determinant form for the degenerate Sheffer sequences is investigated as a function of degenerate polynomial sequences of binomial type. Determinant forms and other properties for some members including the degenerate Poisson-Charlier, Korobov and degenerate actuarial sequences are also obtained. Further, the multi-variable degenerate Hermite-Sheffer sequences are introduced via determinants. Finally, the numerical results showing the approximate solutions of degenerate members and their hybrid forms are mentioned. The distribution of zeros is depicted via graphs.

Keywords: Sheffer sequences; Degenerate Sheffer sequences; Degenerate Hermite-Sheffer sequences; Hessenberg determinant; Approximate solutions; 11B83; 15A15; 33-04; 33F05; 33E99 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s13226-023-00490-3

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