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AIMS Mathematics

2024, Volume 9, Issue 9: 25145-25165. doi: 10.3934/math.20241226
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Properties and applications of generalized 1-parameter 3-variable Hermite-based Appell polynomials

  • 1.
    Mathematics Department, College of Science, King Khalid University, Abha 61413, Saudi Arabia
  • 2.
    Symbiosis Institute of Technology, Pune Campus, Symbiosis International (Deemed University), Pune, India
  • Received: 27 May 2024 Revised: 19 July 2024 Accepted: 30 July 2024 Published: 28 August 2024

  • MSC : 33E20, 33C45, 33B10, 33E30, 39A14, 45J05, 11T23

  • We present a novel framework for introducing generalized 3-variable 1-parameter Hermite-based Appell polynomials. These polynomials are characterized by generating function, series definition, and determinant definition, elucidating their fundamental properties. Moreover, utilizing a factorization method, we established recurrence relations, shift operators, and various differential equations, including differential, integrodifferential, and partial differential equations. Special attention is given to exploring the specific cases of 3-variable 1-parameter generalized Hermite-based Bernoulli, Euler, and Genocchi polynomials, offering insights into their unique features and applications.

    Citation: Mohra Zayed, Shahid Ahmad Wani. Properties and applications of generalized 1-parameter 3-variable Hermite-based Appell polynomials[J]. AIMS Mathematics, 2024, 9(9): 25145-25165. doi: 10.3934/math.20241226

    Related Papers:

  • We present a novel framework for introducing generalized 3-variable 1-parameter Hermite-based Appell polynomials. These polynomials are characterized by generating function, series definition, and determinant definition, elucidating their fundamental properties. Moreover, utilizing a factorization method, we established recurrence relations, shift operators, and various differential equations, including differential, integrodifferential, and partial differential equations. Special attention is given to exploring the specific cases of 3-variable 1-parameter generalized Hermite-based Bernoulli, Euler, and Genocchi polynomials, offering insights into their unique features and applications.



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