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

✍ Scribed by Ulrich Abel

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 150 KB
• Volume: 97
• Category: Article
• ISSN: 0021-9045
• DOI: 10.1006/jath.1997.3253

✦ Synopsis

The concern of this paper is a recent generalization L n ( f (t 1 , t 2 ); 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 operators L n as n tends to infinity. The result is in a form convenient for applications. All coefficients of n &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 operators L n . The result for the one-dimensional case was previously derived by the author.