Representing with probabilistic ordered Bell and degenerate ordered Bell polynomials

IF 2.6 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics Pub Date : 2025-09-30 DOI:10.1016/j.cam.2025.117122

Dae San Kim , Taekyun Kim

引用次数: 0

Abstract

This paper explores the representation of arbitrary polynomials in terms of probabilistic ordered Bell polynomials and probabilistic degenerate ordered Bell polynomials associated with a random variable

Y

, whose moment generating function exists in a neighborhood of the origin. We extend this investigation to their higher-order counterparts. Employing umbral calculus, we derive explicit formulas and illustrate our findings with relevant examples.

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用概率有序贝尔多项式和退化有序贝尔多项式表示

本文探讨了任意多项式的概率有序贝尔多项式和概率退化有序贝尔多项式与随机变量Y的关系，随机变量Y的矩生成函数存在于原点的邻域内。我们将调查扩展到他们的高阶同行。利用本影演算，我们推导出显式公式，并用相关的例子说明我们的发现。

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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来源期刊

Journal of Computational and Applied Mathematics 数学-应用数学

CiteScore

5.40

自引率

4.20%

发文量

437

审稿时长

3.0 months

期刊介绍： The Journal of Computational and Applied Mathematics publishes original papers of high scientific value in all areas of computational and applied mathematics. The main interest of the Journal is in papers that describe and analyze new computational techniques for solving scientific or engineering problems. Also the improved analysis, including the effectiveness and applicability, of existing methods and algorithms is of importance. The computational efficiency (e.g. the convergence, stability, accuracy, ...) should be proved and illustrated by nontrivial numerical examples. Papers describing only variants of existing methods, without adding significant new computational properties are not of interest. The audience consists of: applied mathematicians, numerical analysts, computational scientists and engineers.