Confluent Appell Polynomials of Class $A^{\left( 2\right)} $ and Generalization to Sz\'asz Operators

Abstract

In this paper, we define confluent Appell polynomials of class $A^{\left(2\right) }$, construct a generalization of Sz\'asz operators using these polyomials and derive some approximation properties of this generalization on the semi infinite interval in a weighted function space. Finally, some graphical results are given to show the approximation process by using Maple algoritms of constructed operators to a given function $f$.