Representations by ordered Bell and degenerate ordered Bell polynomials
Dae san Kim, Taekyun Kim
TL;DR
This paper develops explicit formulas for representing polynomials using ordered Bell and degenerate ordered Bell polynomials, extending to higher orders with umbral calculus techniques.
Contribution
It introduces new explicit formulas for polynomial representations in terms of ordered Bell and degenerate ordered Bell polynomials, including higher-order cases.
Findings
Derived explicit formulas for polynomial representations
Extended results to higher-order ordered Bell polynomials
Illustrated formulas with examples
Abstract
In this paper, we consider the problem of representing any polynomial in terms of the ordered Bell and degenerate ordered Bell polynomials, and more generally of the higher-order ordered Bell and higher-order degenerate ordered Bell polynomials. We derive explicit formulas with the help of umbral calculus and illustrate our results with some examples.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Advanced Mathematical Identities · Nonlinear Waves and Solitons