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

Mumtaz Riyasat (), Amal S. Alali, Shahid Ahmad Wani and Subuhi Khan
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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

Mathematics, 2024, vol. 12, issue 17, 1-23

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.

Keywords: Legendre polynomials; Hermite polynomials; Legendre-Hermite polynomials; Apostol type Legendre-Hermite Frobenius-Euler polynomials (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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