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arXiv · 2608.16272

Complete asymptotic expansion for a Durrmeyer variant of operators based on Hermite polynomials

Ulrich Abel·Naim L. Braha
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Abstract

In this paper, we study a Durrmeyer variant of the positive linear operators based on two-variable Hermite polynomials recently introduced by G. Krech (2016). Our main objective is to establish a complete asymptotic expansion for these operators as n tends to infinity for locally integrable functions of polynomial growth. The coefficients of the expansion are explicitly expressed in terms of the derivatives of the function. As a corollary, a Voronovskaja-type formula is obtained.

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Ulrich Abel, Naim L. Braha. 2026-08-17. Complete asymptotic expansion for a Durrmeyer variant of operators based on Hermite polynomials. https://arxiv.org/abs/2608.16272

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