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<p>In the present paper, we study the asymptotic properties of the semi-exponential Post–Widder operator. It is connected with the power function <i>p</i>, <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(p\left( x\right) =x^{2}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>p</mi> <mfenced close=")" open="("> <mi>x</mi> </mfenced> <mo>=</mo> <msup> <mi>x</mi> <mn>2</mn> </msup> </mrow> </math></EquationSource> </InlineEquation>. 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.</p>

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

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  • 发表日期：

    2026年3月24日

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  • Ulrich Abel,
  • Octavian Agratini,
  • Radu Păltănea

摘要

In the present paper, we study the asymptotic properties of the semi-exponential Post–Widder operator. It is connected with the power function p, \(p\left( x\right) =x^{2}\) 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.