Properties and applications of Bell polynomials of two variables

Abstract

In this article, we introduce Bell polynomials of two variables within the framework of generating functions and explore various properties associated with them. Specifically, we delve into explicit representations, summation formulae, recurrence relations, and addition formulas. Additionally, we present the matrix form and product formula for these polynomials. Finally, we introduce the two-variable Bell-based Stirling polynomials of the second kind and outline their corresponding results. This study contributes to a deeper understanding of the properties and applications of Bell polynomials in mathematical analysis.