An application of the partial r-Bell polynomials on some family of bivariate polynomials

Abstract

The aim of this paper is to give some combinatorial relations linked polynomials generalizing those of Appell type to the partial r-Bell polynomials. We give an inverse relation, recurrence relations involving some family of polynomials and their exact expressions at rational values in terms of the partial r-Bell polynomials. We illustrate the obtained results by various comprehensive examples.