On the Asymptotic Approximation with Bivariate Operators of Bleimann, Butzer, and Hahn Original Research Article

The concern of this paper is a recent generalizationLn(f(t1, t2); x, y) for the operators of Bleimann, Butzer, and Hahn in two variables which is distinct from a tensor product. We present the complete asymptotic expansion for the operatorsLnasntends to infinity. The result is in a form convenient for applications. All coefficients ofn−k(k=1, 2, …) are calculated explicitly in terms of Stirling numbers of the first and second kind. As a special case we obtain a Voronovskaja-type theorem for the operatorsLn. The result for the one-dimensional case was previously derived by the author.