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 , $$p\left( x\right) =x^{2}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>p</mml:mi> <mml:mfenced> <mml:mi>x</mml:mi> </mml:mfenced> <mml:mo>=</mml:mo> <mml:msup> <mml:mi>x</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:mrow> </mml:math> . 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.