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<p>In the domain of specialized mathematical functions, the rising interest in <i>q</i>-calculus continues to attract researchers, offering powerful tools for modeling in fields like quantum computing, non-commutative probability, combinatorics, functional analysis, mathematical physics, and approximation theory. This study introduces the framework of multivariate <i>q</i>-Hermite-based Appell polynomials, employing various <i>q</i>-calculus techniques. Key properties and fresh insights into these polynomials are examined, such as their generating functions, series representations, recurrence relations, <i>q</i>-differential identities, and operational mechanisms. Additionally, it is shown that these polynomials maintain a quasi-monomial structure within the <i>q</i>-calculus context.</p>

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Multivariate q-Hermite-based Appell polynomials: structural properties and applications

  • 期刊论文

  • 发表日期：

    2025年5月4日

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  • Shahid Ahmad Wani,
  • Mumtaz Riyasat,
  • Ramírez William,
  • Waseem Ahmad Khan

摘要

In the domain of specialized mathematical functions, the rising interest in q-calculus continues to attract researchers, offering powerful tools for modeling in fields like quantum computing, non-commutative probability, combinatorics, functional analysis, mathematical physics, and approximation theory. This study introduces the framework of multivariate q-Hermite-based Appell polynomials, employing various q-calculus techniques. Key properties and fresh insights into these polynomials are examined, such as their generating functions, series representations, recurrence relations, q-differential identities, and operational mechanisms. Additionally, it is shown that these polynomials maintain a quasi-monomial structure within the q-calculus context.