A complete asymptotic expansion for the semi-exponential Post–Widder operators

Abstract

In the present paper, we study the asymptotic properties of the semi-exponential Post–Widder operator. It is connected with the power function p, \(p\left( x\right) =x^{2}\). The main result is a pointwise complete asymptotic expansion valid for locally smooth functions of exponential growth. All coefficients are derived and explicitly given. As a special case we recover the complete asymptotic expansion for the classical Post–Widder operator.