Advances in the generalized Ces`aro polynomials

Abstract

Ces`aro polynomials have been extended in various ways and applied in diverse areas. In this paper, we aim to introduce a multivariable and multiparameter generalization of Ces`aro polynomials. Then we explore several generating functions, an addition formula, a differential-recurrence relation, a multiple integral formula for this extended Ces`aro polynomial, as well as a multiple integral formula whose kernel is this extended Ces`aro polynomial. Also we present several bilinear and bilateral generating functions for this extended Ces`aro polynomial, two of whose examples are demonstrated.