The differential mean value of divided differences

被引：8

作者：

Abel, Ulrich

Ivan, Mircea

机构：

[1] Univ Appl Sci, Fachbereich MND, Fachhsch Giessen Friedberg, D-61169 Friedberg, Germany

[2] Tech Univ Cluj Napoca, Dept Math, Cluj Napoca 400020, Romania

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2007年 / 325卷 / 01期

关键词：

divided differences; differentiation; mean value theorems; asymptotic approximations; asymptotic expansions;

D O I：

10.1016/j.jmaa.2006.01.088

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The paper deals with the asymptotic behaviour of the differential mean value of divided differences as the interval shrinks to zero by presenting an asymptotic expansion. The coefficients are given by a recurrence formula. For a wide class of analytic functions the differential mean value can be represented by a convergent sum. Our results generalize two recent theorems by Powers, Riedel and Sahoo [R.C. Powers, T. Riedel, RK. Sahoo, Limit properties of differential mean values, J. Math. Anal. Appl. 227 (1998) 216-226]. (c) 2006 Elsevier Inc. All rights reserved.

引用

页码：560 / 570

页数：11

共 6 条

[1]

Abel U, 2005, J COMPUT ANAL APPL, V7, P89

[2] On the Lagrange remainder of the Taylor formula [J].