Degenerate poly-Bell polynomials and numbers

Abstract Numerous mathematicians have studied ‘poly’ as one of the generalizations to special polynomials, such as Bernoulli, Euler, Cauchy, and Genocchi polynomials. In relation to this, in this paper, we introduce the degenerate poly-Bell polynomials emanating from the degenerate polyexponential f...

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Bibliographic Details
Main Authors: Taekyun Kim, Hye Kyung Kim
Format: Article
Language:English
Published: SpringerOpen 2021-07-01
Series:Advances in Difference Equations
Subjects:
Online Access:https://doi.org/10.1186/s13662-021-03522-6
Description
Summary:Abstract Numerous mathematicians have studied ‘poly’ as one of the generalizations to special polynomials, such as Bernoulli, Euler, Cauchy, and Genocchi polynomials. In relation to this, in this paper, we introduce the degenerate poly-Bell polynomials emanating from the degenerate polyexponential functions which are called the poly-Bell polynomials when λ → 0 $\lambda \rightarrow 0$ . Specifically, we demonstrate that they are reduced to the degenerate Bell polynomials if k = 1 $k = 1$ . We also provide explicit representations and combinatorial identities for these polynomials, including Dobinski-like formulas, recurrence relationships, etc.
ISSN:1687-1847