Systematic Exploration of q $$ q $$ -Truncated-Fubini–Appell Polynomials with Computational Applications

IF 2 3区数学 Q1 MATHEMATICS, APPLIED

Mathematical Methods in the Applied Sciences Pub Date : 2026-10-07 Epub Date: 2026-07-29 DOI:10.1002/mma.70920

Abdulghani Muhyi, L. M. Abdalgadir, Amel Touati, Khaled Aldwoah

{"title":"Systematic Exploration of \n \n \n q\n \n \n$$ q $$\n\n -Truncated-Fubini–Appell Polynomials with Computational Applications","authors":"Abdulghani Muhyi, L. M. Abdalgadir, Amel Touati, Khaled Aldwoah","doi":"10.1002/mma.70920","DOIUrl":null,"url":null,"abstract":"<div>\n \n This article systematically investigates a new family of <math>\n \n <semantics>\n \n <mrow>\n \n <mi>q</mi>\n </mrow>\n \n <annotation>\n$$ q $$\n</annotation>\n </semantics>\n </math>-special functions: the <math>\n \n <semantics>\n \n <mrow>\n \n <mi>q</mi>\n </mrow>\n \n <annotation>\n$$ q $$\n</annotation>\n </semantics>\n </math>-truncated-Fubini–Appell polynomials. We first define the fundamental <math>\n \n <semantics>\n \n <mrow>\n \n <mi>q</mi>\n </mrow>\n \n <annotation>\n$$ q $$\n</annotation>\n </semantics>\n </math>-truncated-Fubini polynomials through their generating function and establish their basic properties. For the extended family, we then develop explicit series representations, <math>\n \n <semantics>\n \n <mrow>\n \n <mi>q</mi>\n </mrow>\n \n <annotation>\n$$ q $$\n</annotation>\n </semantics>\n </math>-recurrence relations, <math>\n \n <semantics>\n \n <mrow>\n \n <mi>q</mi>\n </mrow>\n \n <annotation>\n$$ q $$\n</annotation>\n </semantics>\n </math>-integral formulas, quasi-monomial properties, differential equations, and a determinant representation. Applying this general theory yields specific results for notable cases such as the <math>\n \n <semantics>\n \n <mrow>\n \n <mi>q</mi>\n </mrow>\n \n <annotation>\n$$ q $$\n</annotation>\n </semantics>\n </math>-truncated-Fubini–Bernoulli and Euler polynomials. Finally, a computational study using Mathematica offers visual and numerical analysis of the polynomials' zero distributions, providing support for the theoretical results.\n </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"49 16","pages":"17190-17213"},"PeriodicalIF":2.0000,"publicationDate":"2026-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Methods in the Applied Sciences","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/mma.70920","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2026/7/29 0:00:00","PubModel":"Epub","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 0

Abstract

This article systematically investigates a new family of $q$ -special functions: the $q$ -truncated-Fubini–Appell polynomials. We first define the fundamental $q$ -truncated-Fubini polynomials through their generating function and establish their basic properties. For the extended family, we then develop explicit series representations, $q$ -recurrence relations, $q$ -integral formulas, quasi-monomial properties, differential equations, and a determinant representation. Applying this general theory yields specific results for notable cases such as the $q$ -truncated-Fubini–Bernoulli and Euler polynomials. Finally, a computational study using Mathematica offers visual and numerical analysis of the polynomials' zero distributions, providing support for the theoretical results.

查看原文本刊更多论文

q $$ q $$ -截断-富比尼-阿佩尔多项式的系统探索及其计算应用

本文系统地研究了一类新的q $$ q $$特殊函数：q $$ q $$截断的fubini - appell多项式。首先通过生成函数定义了基本的q $$ q $$ -截断-富比尼多项式，并建立了它们的基本性质。对于扩展族，我们随后开发了显式级数表示，q $$ q $$ -递归关系，q $$ q $$ -积分公式，拟单项式性质，微分方程和行列式表示。应用这一一般理论可以得到一些特殊的结果，例如q $$ q $$ -截断-富比尼-伯努利多项式和欧拉多项式。最后，利用Mathematica软件对多项式的零分布进行了可视化和数值分析，为理论结果提供了支持。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Mathematical Methods in the Applied Sciences 数学-应用数学

CiteScore

4.90

自引率

6.90%

发文量

798

审稿时长

6 months

期刊介绍： Mathematical Methods in the Applied Sciences publishes papers dealing with new mathematical methods for the consideration of linear and non-linear, direct and inverse problems for physical relevant processes over time- and space- varying media under certain initial, boundary, transition conditions etc. Papers dealing with biomathematical content, population dynamics and network problems are most welcome. Mathematical Methods in the Applied Sciences is an interdisciplinary journal: therefore, all manuscripts must be written to be accessible to a broad scientific but mathematically advanced audience. All papers must contain carefully written introduction and conclusion sections, which should include a clear exposition of the underlying scientific problem, a summary of the mathematical results and the tools used in deriving the results. Furthermore, the scientific importance of the manuscript and its conclusions should be made clear. Papers dealing with numerical processes or which contain only the application of well established methods will not be accepted. Because of the broad scope of the journal, authors should minimize the use of technical jargon from their subfield in order to increase the accessibility of their paper and appeal to a wider readership. If technical terms are necessary, authors should define them clearly so that the main ideas are understandable also to readers not working in the same subfield.