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<p>Motivated by Ismail and Zhang [Trans. Amer. Math. Soc., 2017, 369: 6779–6821], we introduce two generalized <i>q</i>-2D ultraspherical polynomials and deduce their corresponding <i>q</i>-partial differential equations. In addition, bilinear and multilinear generating functions for the generalized <i>q</i>-2D ultraspherical polynomials are deduced by the method of <i>q</i>-partial differential equations, which generalize results of Ismail and Zhang. Moreover, a new transformational identity and involving <i>q</i>-2D ultraspherical polynomials and linear relations for <i>q</i>-2D ultraspherical polynomials are obtained.</p>

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q-Partial Differential Equations for Generalized q-2D Ultraspherical Polynomials with Some Applications

  • 期刊论文

  • 发表日期：

    2026年5月20日

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  • Jian Cao

摘要

Motivated by Ismail and Zhang [Trans. Amer. Math. Soc., 2017, 369: 6779–6821], we introduce two generalized q-2D ultraspherical polynomials and deduce their corresponding q-partial differential equations. In addition, bilinear and multilinear generating functions for the generalized q-2D ultraspherical polynomials are deduced by the method of q-partial differential equations, which generalize results of Ismail and Zhang. Moreover, a new transformational identity and involving q-2D ultraspherical polynomials and linear relations for q-2D ultraspherical polynomials are obtained.