基于埃尔米特多项式的算子的Durrmeyer变体的完全渐近展开
Complete asymptotic expansion for a Durrmeyer variant of operators based on Hermite polynomials
AI总结：
本文研究G. Krech 2016年提出的基于二元埃尔米特多项式的正线性算子的Durrmeyer变体，建立其针对多项式增长局部可积函数的完全渐近展开，系数用函数导数明确表示，还得到Voronovskaja型公式。
AI中文摘要：
本文研究了G. Krech（2016）新近引入的基于二元埃尔米特多项式的正线性算子的Durrmeyer变体。我们的主要目标是针对多项式增长的局部可积函数，建立这些算子当n趋于无穷时的完全渐近展开，展开的系数用函数的导数明确表示。作为推论，得到了一个Voronovskaja型公式。
英文摘要：
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.
