Degenerate 2D bivariate Appell polynomials: properties and applications

Abstract

The development of certain aspects of hybrid special polynomials after incorporating monomiality principle, operational rules, and other properties and their aspects is obvious and indisputable. The study presented in this paper follows this line of research. By using the monomiality principle, new outcomes are produced, thus in line with prior facts, our aim is to introduce the degenerate 2D bivariate Appell polynomials $ \mathbb {R}^{m}_j(u,v;h) $ . Further, we obtain some well-known main properties and explicit forms satisfied by these polynomials. Also, generating relations corresponding to the degenerate 2D bivariate Bernoulli, Euler, and Genocchi polynomials are established, they will further be helpful in establishing the corresponding results for these polynomials.

Keywords

• degenerate 2d bivariate appell polynomials
• monomiality principle
• explicit forms
• determinant form