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

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.