Advances in the generalized Cesàro polynomials

Abstract

Cesàro 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 Cesàro polynomials. Then we explore several generating functions, an addition formula, a differential-recurrence relation, a multiple integral formula for this extended Cesàro polynomial, as well as a multiple integral formula whose kernel is this extended Cesàro polynomial. Also we present several bilinear and bilateral generating functions for this extended Ces`aro polynomial, two of whose examples are demonstrated.

Keywords

• Cesàro polynomials
• generating function
• recurrence relation
• hypergeometric function
• integral representation