Corrected Euler-Maclaurin's formulae

被引：12

作者：

Franjić I. ^{[1
]}

Pečarić J. ^{[2
]}

机构：

[1] Faculty of Food Technology and Biotechnology, Department of mathematics, University of Zagreb, 10000 Zagreb

[2] Faculty of Textile Technology, University of Zagreb, 10000 Zagreb

来源：

Rendiconti del Circolo Matematico di Palermo | 2005年 / 54卷 / 2期

关键词：

Bernoulli polynomials; corrected Maclaurin's formula; functions of bounded variation; Lipschitzian functions; open type quadrature formulae;

D O I：

10.1007/BF02874640

中图分类号：

学科分类号：

摘要：

The aim of this paper is to derive corrected Euler-Maclaurin's formulae, i. e. open type quadrature formulae where the integral is approximated not only with the values of the function in points (5a+b)/6, (a+b)/2 and (a+5b)/6, but also with values of the first derivative in end points of the interval. These formulae will have a higher degree of exactness than the ones obtained in [2]. Using the derived formulae, a number of inequalities for various classes of functions are obtained. © 2005 Springer.

引用

页码：259 / 272

页数：13

共 8 条

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[2]

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[3]

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[4]

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[5]

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[6]

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[7]

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[8]

Matic M., Improvement of some inequalities of Euler-Grüs type, Computers and Mathematics with Applications, 46, pp. 1325-1336, (2003)

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