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Several Characterizations of the Generalized 1-Parameter 3-Variable Hermite Polynomials

Author

Listed:
  • Shahid Ahmad Wani

    (Symbiosis Institute of Technology, Pune Campus, Symbiosis International (Deemed University), Pune 412115, India)

  • Khalil Hadi Hakami

    (Department of Mathematics, Faculty of Science, Jazan University, P.O. Box 2097, Jazan 45142, Saudi Arabia)

  • Hamad Zogan

    (Department of Computer Science, College of Engineering and Computer Science, Jazan University, Jazan 45142, Saudi Arabia)

Abstract

This paper presents a novel framework for introducing generalized 1-parameter 3-variable Hermite polynomials. These polynomials are characterized through generating functions and series definitions, elucidating their fundamental properties. Moreover, utilising a factorisation method, this study establishes recurrence relations, shift operators, and various differential equations, including differential, integro-differential, and partial differential equations.

Suggested Citation

  • Shahid Ahmad Wani & Khalil Hadi Hakami & Hamad Zogan, 2024. "Several Characterizations of the Generalized 1-Parameter 3-Variable Hermite Polynomials," Mathematics, MDPI, vol. 12(16), pages 1-15, August.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:16:p:2459-:d:1452729
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    References listed on IDEAS

    as
    1. Subuhi Khan & Nusrat Raza, 2013. "General-Appell Polynomials within the Context of Monomiality Principle," International Journal of Analysis, Hindawi, vol. 2013, pages 1-11, February.
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