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 (x) =x^2 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.
Abel et al. (Tue,) studied this question.