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A Note on q-partial Differential Equations for Generalized q-2D Hermite Polynomials

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Progress on Difference Equations and Discrete Dynamical Systems (ICDEA 2019)

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Abstract

In this short paper, we generalize Ismail–Zhang’s q-2D Hermite polynomials (Trans Am Math Soc 369:6779–6821 (2017), [14]) with an extra parameter and prove that if an analytic function in several variables satisfies a set of partial differential equations of second order, then it can be expanded in terms of the product of the generalized q-2D Hermite polynomials. In addition, we give some generating functions as applications.

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Acknowledgments

The first author thanks the professor Steve Baigent of University College London for the hospitality during the ICDEA 2019 when the major part of this work was carried out. This work was supported by the Zhejiang Provincial Natural Science Foundation of China (No. LY21A010019) and the National Natural Science Foundation of China (No. 12071421).

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Authors and Affiliations

  1. Department of Mathematics, Hangzhou Normal University, Hangzhou, 311121, Zhejiang, China

    JIAN CAO & Li-Ping Cai

  2. Department of Mathematics, Zhejiang University, Hangzhou, 310027, China

    Tianxin Cai

Authors
  1. JIAN CAO
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  2. Tianxin Cai
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  3. Li-Ping Cai
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Corresponding author

Correspondence to JIAN CAO .

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Editors and Affiliations

  1. Department of Mathematics, University College London, London, UK

    Steve Baigent

  2. Department of Mathematics and Statistics, Missouri University of Science and Technology, Rolla, MO, USA

    Martin Bohner

  3. Department of Mathematics, Trinity University, San Antonio, TX, USA

    Saber Elaydi

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CAO, J., Cai, T., Cai, LP. (2020). A Note on q-partial Differential Equations for Generalized q-2D Hermite Polynomials. In: Baigent, S., Bohner, M., Elaydi, S. (eds) Progress on Difference Equations and Discrete Dynamical Systems. ICDEA 2019. Springer Proceedings in Mathematics & Statistics, vol 341. Springer, Cham. https://doi.org/10.1007/978-3-030-60107-2_8

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