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Properties of Multivariate Hermite Polynomials in Correlation with Frobenius–Euler Polynomials

Author

Listed:
  • Mohra Zayed

    (Mathematics Department, College of Science, King Khalid University, Abha 61413, Saudi Arabia
    These authors contributed equally to this work.)

  • Shahid Ahmad Wani

    (Department of Applied Sciences, Symbiosis Institute of Technology, Symbiosis International (Deemed University) (SIU), Lavale, Pune 412115, Maharashtra, India
    These authors contributed equally to this work.)

  • Yamilet Quintana

    (Departamento de Matemáticas, Universidad Carlos III de Madrid, Avenida de la Universidad 30, Leganés, 28911 Madrid, Spain
    Instituto de Ciencias Matemáticas (ICMAT), Campus de Cantoblanco UAM, 28049 Madrid, Spain
    These authors contributed equally to this work.)

Abstract

A comprehensive framework has been developed to apply the monomiality principle from mathematical physics to various mathematical concepts from special functions. This paper presents research on a novel family of multivariate Hermite polynomials associated with Apostol-type Frobenius–Euler polynomials. The study derives the generating expression, operational rule, differential equation, and other defining characteristics for these polynomials. Additionally, the monomiality principle for these polynomials is verified. Moreover, the research establishes series representations, summation formulae, and operational and symmetric identities, as well as recurrence relations satisfied by these polynomials.

Suggested Citation

  • Mohra Zayed & Shahid Ahmad Wani & Yamilet Quintana, 2023. "Properties of Multivariate Hermite Polynomials in Correlation with Frobenius–Euler Polynomials," Mathematics, MDPI, vol. 11(16), pages 1-17, August.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:16:p:3439-:d:1212700
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    References listed on IDEAS

    as
    1. Taekyun Kim & Byungje Lee, 2009. "Some Identities of the Frobenius-Euler Polynomials," Abstract and Applied Analysis, Hindawi, vol. 2009, pages 1-7, March.
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    Cited by:

    1. Shahid Ahmad Wani & Georgia Irina Oros & Ali M. Mahnashi & Waleed Hamali, 2023. "Properties of Multivariable Hermite Polynomials in Correlation with Frobenius–Genocchi Polynomials," Mathematics, MDPI, vol. 11(21), pages 1-17, November.
    2. Mumtaz Riyasat & Amal S. Alali & Shahid Ahmad Wani & Subuhi Khan, 2024. "On Convoluted Forms of Multivariate Legendre-Hermite Polynomials with Algebraic Matrix Based Approach," Mathematics, MDPI, vol. 12(17), pages 1-23, August.

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