Bivariate Kind of Generalized Laguerre-Based Appell Polynomials with Applications to Special Polynomials

Abstract

In this paper, we introduce a new generalization of Laguerre and Laguerre-based Appell polynomials and investigate their fundamental properties. We derive a recurrence relation, multiplicative and derivative operators, and differential equation by verifying quasi-monomiality. Also, the series representation and determinant representation for this novel polynomial family are established. Furthermore, we define subpolynomials within this framework, namely generalized Laguerre-Hermite Appell polynomials and establish their corresponding results. Additionally, Laguerre-Hermite-Bernoulli, Euler and Genocchi polynomials are obtained, and explore their structural and operational characteristics. The results obtained contribute to the broader study of special polynomials and their applications in mathematical physics and differential equations.