{"title":"与随机变量相关的概率退化富比尼多项式","authors":"Rongrong Xu, Taekyun Kim, Dae San Kim, Yuankui Ma","doi":"10.1007/s44198-024-00210-3","DOIUrl":null,"url":null,"abstract":"<p>Let <i>Y</i> be a random variable such that the moment generating function of <i>Y</i> exists in a neighborhood of the origin. The aim of this paper is to study probabilistic versions of the degenerate Fubini polynomials and the degenerate Fubini polynomials of order <i>r</i>, namely the probabilisitc degenerate Fubini polynomials associated with <i>Y</i> and the probabilistic degenerate Fubini polynomials of order <i>r</i> associated with <i>Y</i>. We derive some properties, explicit expressions, certain identities and recurrence relations for those polynomials. As special cases of <i>Y</i>, we treat the gamma random variable with parameters <span>\\(\\alpha ,\\beta > 0\\)</span>, the Poisson random variable with parameter <span>\\(\\alpha > 0\\)</span>, and the Bernoulli random variable with probability of success <i>p</i>.</p>","PeriodicalId":48904,"journal":{"name":"Journal of Nonlinear Mathematical Physics","volume":"2016 1","pages":""},"PeriodicalIF":1.4000,"publicationDate":"2024-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Probabilistic Degenerate Fubini Polynomials Associated with Random Variables\",\"authors\":\"Rongrong Xu, Taekyun Kim, Dae San Kim, Yuankui Ma\",\"doi\":\"10.1007/s44198-024-00210-3\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>Let <i>Y</i> be a random variable such that the moment generating function of <i>Y</i> exists in a neighborhood of the origin. The aim of this paper is to study probabilistic versions of the degenerate Fubini polynomials and the degenerate Fubini polynomials of order <i>r</i>, namely the probabilisitc degenerate Fubini polynomials associated with <i>Y</i> and the probabilistic degenerate Fubini polynomials of order <i>r</i> associated with <i>Y</i>. We derive some properties, explicit expressions, certain identities and recurrence relations for those polynomials. As special cases of <i>Y</i>, we treat the gamma random variable with parameters <span>\\\\(\\\\alpha ,\\\\beta > 0\\\\)</span>, the Poisson random variable with parameter <span>\\\\(\\\\alpha > 0\\\\)</span>, and the Bernoulli random variable with probability of success <i>p</i>.</p>\",\"PeriodicalId\":48904,\"journal\":{\"name\":\"Journal of Nonlinear Mathematical Physics\",\"volume\":\"2016 1\",\"pages\":\"\"},\"PeriodicalIF\":1.4000,\"publicationDate\":\"2024-07-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Nonlinear Mathematical Physics\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.1007/s44198-024-00210-3\",\"RegionNum\":4,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Nonlinear Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1007/s44198-024-00210-3","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
摘要
设 Y 是随机变量,且 Y 的矩生成函数存在于原点附近。本文旨在研究退化富比尼多项式和 r 阶退化富比尼多项式的概率版本,即与 Y 相关的概率退化富比尼多项式和与 Y 相关的概率退化富比尼多项式。作为 Y 的特例,我们处理了参数为 \(\alpha ,\beta > 0\) 的伽马随机变量、参数为 \(\alpha > 0\) 的泊松随机变量和成功概率为 p 的伯努利随机变量。
Probabilistic Degenerate Fubini Polynomials Associated with Random Variables
Let Y be a random variable such that the moment generating function of Y exists in a neighborhood of the origin. The aim of this paper is to study probabilistic versions of the degenerate Fubini polynomials and the degenerate Fubini polynomials of order r, namely the probabilisitc degenerate Fubini polynomials associated with Y and the probabilistic degenerate Fubini polynomials of order r associated with Y. We derive some properties, explicit expressions, certain identities and recurrence relations for those polynomials. As special cases of Y, we treat the gamma random variable with parameters \(\alpha ,\beta > 0\), the Poisson random variable with parameter \(\alpha > 0\), and the Bernoulli random variable with probability of success p.
期刊介绍:
Journal of Nonlinear Mathematical Physics (JNMP) publishes research papers on fundamental mathematical and computational methods in mathematical physics in the form of Letters, Articles, and Review Articles.
Journal of Nonlinear Mathematical Physics is a mathematical journal devoted to the publication of research papers concerned with the description, solution, and applications of nonlinear problems in physics and mathematics.
The main subjects are:
-Nonlinear Equations of Mathematical Physics-
Quantum Algebras and Integrability-
Discrete Integrable Systems and Discrete Geometry-
Applications of Lie Group Theory and Lie Algebras-
Non-Commutative Geometry-
Super Geometry and Super Integrable System-
Integrability and Nonintegrability, Painleve Analysis-
Inverse Scattering Method-
Geometry of Soliton Equations and Applications of Twistor Theory-
Classical and Quantum Many Body Problems-
Deformation and Geometric Quantization-
Instanton, Monopoles and Gauge Theory-
Differential Geometry and Mathematical Physics