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On Convoluted Forms of Multivariate Legendre-Hermite Polynomials with Algebraic Matrix Based Approach

Author

Listed:
  • Mumtaz Riyasat

    (Department of Applied Mathematics, Faculty of Engineering and Technology, Aligarh Muslim University, Aligarh 202001, India)

  • Amal S. Alali

    (Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia)

  • Shahid Ahmad Wani

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

  • Subuhi Khan

    (Department of Mathematics, Aligarh Muslim University, Aligarh 202001, India)

Abstract

The main purpose of this article is to construct a new class of multivariate Legendre-Hermite-Apostol type Frobenius-Euler polynomials. A number of significant analytical characterizations of these polynomials using various generating function techniques are provided in a methodical manner. These enactments involve explicit relations comprising Hurwitz-Lerch zeta functions and λ -Stirling numbers of the second kind, recurrence relations, and summation formulae. The symmetry identities for these polynomials are established by connecting generalized integer power sums, double power sums and Hurwitz-Lerch zeta functions. In the end, these polynomials are also characterized Svia an algebraic matrix based approach.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:17:p:2662-:d:1465317
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    References listed on IDEAS

    as
    1. 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.
    2. Khan, Subuhi & Riyasat, Mumtaz, 2015. "Determinantal approach to certain mixed special polynomials related to Gould–Hopper polynomials," Applied Mathematics and Computation, Elsevier, vol. 251(C), pages 599-614.
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