Scholarlink

<p>The generalization of the monomiality principle for <i>q</i>-special polynomials has just been explained and demonstrated. This extension is used to study the monomiality features of the number of <i>q</i>-special polynomials, such as <i>q</i>-Appell polynomials, <i>q</i>-Gould–Hopper polynomials, two variables <i>q</i>-Hermite, <i>q</i>-Laguerre and <i>q</i>-Legendre polynomials. Additionally, several kinds of hybrid <i>q</i>-special polynomials and their monomiality features are studied, such as two-variable <i>q</i>-Laguerre-Appell polynomials, two-variable based <i>q</i>-Hermite-Appell polynomials and <i>q</i>-Gould–Hopper–Appell polynomials. This study seeks to generate the <i>q</i>-Legendre–Gould–Hopper polynomials and then describe their attributes by extending the idea of monomiality for <i>q</i>-polynomials. Furthermore, we propose operational representations, expansion formulae and new families of these polynomials with the aid of <i>q</i>-operational methods and extension for monomiality principle of <i>q</i>-polynomials.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

q-Legendre based Gould–Hopper polynomials and q-operational methods

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2025年4月3日

查看全文
  • Fadel Mohammed,
  • William Ramírez,
  • Clemente Cesarano,
  • Stiven Díaz

摘要

The generalization of the monomiality principle for q-special polynomials has just been explained and demonstrated. This extension is used to study the monomiality features of the number of q-special polynomials, such as q-Appell polynomials, q-Gould–Hopper polynomials, two variables q-Hermite, q-Laguerre and q-Legendre polynomials. Additionally, several kinds of hybrid q-special polynomials and their monomiality features are studied, such as two-variable q-Laguerre-Appell polynomials, two-variable based q-Hermite-Appell polynomials and q-Gould–Hopper–Appell polynomials. This study seeks to generate the q-Legendre–Gould–Hopper polynomials and then describe their attributes by extending the idea of monomiality for q-polynomials. Furthermore, we propose operational representations, expansion formulae and new families of these polynomials with the aid of q-operational methods and extension for monomiality principle of q-polynomials.