About a dubious proof of a correct result about closed Newton Cotes error formulas

IF 1 4区数学 Q1 MATHEMATICS

Open Mathematics Pub Date : 2023-11-24 DOI:10.1515/math-2023-0150

David J. López, Jose A. Padilla, Juan Ruiz, Carlos Tapia, Juan C. Trillo

引用次数: 0

Abstract

In this study, we comment about a wrong proof, at least incomplete, of the closed Newton Cotes error formulas for integration in a closed interval

[ a , b ] .

\left[a,b].

These error formulas appear as an intuitive generalization of the simple proof for the error formula of the trapezoidal rule, and their proofs present one controversial step, which converts the proofs in mischievous, or at least, this step needs a clear clarification that it is not easy to derive. The correct proof of such formulas comes from a technique based on the Peano kernel.

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关于一个关于封闭牛顿柯特误差公式的正确结果的可疑证明

在本研究中，我们评论了闭区间积分的闭牛顿柯特误差公式的一个错误证明，至少是不完整的证明[a, b]。\ [a, b]。这些误差公式是对梯形定则误差公式的简单证明的一种直观的推广，它们的证明有一个有争议的步骤，它把证明变成了恶作剧，或者至少，这一步需要明确说明，它不容易推导。这些公式的正确证明来自一种基于Peano内核的技术。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Open Mathematics MATHEMATICS-

CiteScore

2.40

自引率

5.90%

发文量

审稿时长

16 weeks

期刊介绍： Open Mathematics - formerly Central European Journal of Mathematics Open Mathematics is a fully peer-reviewed, open access, electronic journal that publishes significant, original and relevant works in all areas of mathematics. The journal provides the readers with free, instant, and permanent access to all content worldwide; and the authors with extensive promotion of published articles, long-time preservation, language-correction services, no space constraints and immediate publication. Open Mathematics is listed in Thomson Reuters - Current Contents/Physical, Chemical and Earth Sciences. Our standard policy requires each paper to be reviewed by at least two Referees and the peer-review process is single-blind. Aims and Scope The journal aims at presenting high-impact and relevant research on topics across the full span of mathematics. Coverage includes: