数値積分の漸近展開によるEuler-Maclaurin総和公式の簡単な別証明

Material type: 文書・図像類

Author: 伊野瀬, 崇ほか

Publisher: 愛知工業大学

Publication date: 2000-03-31

Material Format: Digital

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Note (General)：: The Euler-Maclaurin summation formula plays an important role when we yield the correction formulas of numerical integrations or when we make the Romb...

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Material Type: 文書・図像類
Title: 数値積分の漸近展開によるEuler-Maclaurin総和公式の簡単な別証明
Author/Editor: 伊野瀬, 崇
樋口, 功
Author Heading: 伊野瀬, 崇
樋口, 功
Publication, Distribution, etc.: 愛知工業大学
Publication Date: 2000-03-31
Publication Date (W3CDTF): 2000-03-31
Alternative Title: スウチセキブンノゼンキンテンカイニヨル EULER-MACLAURIN ソウワコウシキノカンタンナベツショウメイ
Another simpler proof of Euler-Maclaurin summation formula by the asymptotic expansion of numerical integration
Periodical title: 愛知工業大学研究報告. A, 基礎教育系論文集 = Bulletin of Aichi Institute of Technology. Part A
No. or year of volume/issue: 35
Volume: 35
Pages: 1-10
ISSN (Periodical Title): ISSN : 0387-0804
Text Language Code: jpn
Target Audience: 一般
Note (General): The Euler-Maclaurin summation formula plays an important role when we yield the correction formulas of numerical integrations or when we make the Romberg integration list. But the proof of the above summation formula, given by using the properties of Bernoulli polynomial, is fairly complicated. In this paper, fist we obtain some asymptotic expansions of numerical integration formulas by the terms of the mesuration by parts of higher order derivatives. As an application, we derive so-called end-point correction formulas of mesuration by parts, mid-point rule, trapezoid rule and Simpson's rule independently from the Euler-Maclaurin summation formula. Finally, we shall give an annother simpler and fundamental proof of the Euler-Maclaurin summation formula itself.
identifier:http://repository.aitech.ac.jp/dspace/handle/11133/1987
Access Restrictions: 限定公開
Periodical Title (NCID): AN10455660
https://ci.nii.ac.jp/ncid/AN10455660
Data Provider (Database): 国立情報学研究所 : 学術機関リポジトリデータベース（IRDB）（機関リポジトリ）
https://irdb.nii.ac.jp
Original Data Provider (Database): 愛知工業大学 : 愛知工業大学学術情報リポジトリ