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

In the present paper, we study the asymptotic properties of the semi-exponential Post-Widder operator. It is connected with $p(x)=x^2$. 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.