多伯努利概率多项式和数的明确公式

IF 1.7 3区物理与天体物理 Q2 PHYSICS, MATHEMATICAL

Russian Journal of Mathematical Physics Pub Date : 2024-10-03 DOI:10.1134/S1061920824030087

T. Kim, D. S. Kim

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引用次数: 0

摘要

让 \(Y\) 是一个随机变量，它的矩生成函数存在于原点附近。本文的目的是研究与 \(Y\) 相关的概率伯努利多项式和概率多聚伯努利多项式。它们分别是伯努利多项式和多聚伯努利多项式的概率扩展。我们为它们找到了明确的表达式、某些相关的等式和一些性质。此外，我们还处理了泊松、伽马和伯努利随机变量的特例。 doi 10.1134/s1061920824030087

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Explicit Formulas for Probabilistic Multi-Poly-Bernoulli Polynomials and Numbers

Let \(Y\) be a random variable whose moment generating function exists in a neighborhood of the origin. The aim of this paper is to study probabilistic Bernoulli polynomials of order \(r\) associated with \(Y\) and probabilistic multi-poly-Bernoulli polynomials associated with \(Y\). They are respectively probabilistic extensions of Bernoulli polynomials of order \(r\) and multi-poly-Bernoulli polynomials. We find explicit expressions, certain related identities and some properties for them. In addition, we treat the special cases of Poisson, gamma and Bernoulli random variables.

DOI 10.1134/S1061920824030087

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来源期刊

Russian Journal of Mathematical Physics 物理-物理：数学物理

CiteScore

3.10

自引率

14.30%

发文量

审稿时长

>12 weeks

期刊介绍： Russian Journal of Mathematical Physics is a peer-reviewed periodical that deals with the full range of topics subsumed by that discipline, which lies at the foundation of much of contemporary science. Thus, in addition to mathematical physics per se, the journal coverage includes, but is not limited to, functional analysis, linear and nonlinear partial differential equations, algebras, quantization, quantum field theory, modern differential and algebraic geometry and topology, representations of Lie groups, calculus of variations, asymptotic methods, random process theory, dynamical systems, and control theory.