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<p>In this paper, we establish an umbra for 2-variable <i>q</i>-Hermite polynomials, followed by the introduction of an umbral definition of 3-variable <i>q</i>-Hermite polynomials. Employing umbral techniques, we delved into numerous intriguing properties associated with these polynomials. Additionally, we provide an extension for <i>q</i>-Hermite polynomials as part of our concluding remarks.</p>

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UMBRA AND ITS APPLICATION FOR q-HERMITE POLYNOMIALS

  • 期刊论文

  • 发表日期：

    2025年12月4日

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  • Umme Zainab

摘要

In this paper, we establish an umbra for 2-variable q-Hermite polynomials, followed by the introduction of an umbral definition of 3-variable q-Hermite polynomials. Employing umbral techniques, we delved into numerous intriguing properties associated with these polynomials. Additionally, we provide an extension for q-Hermite polynomials as part of our concluding remarks.