Uncovers complete asymptotic expansions for locally smooth functions, suggesting new insights into operator behavior.
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) =x² 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.
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Abel et al. (2026) studied this question.
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