連続関数の平均値の近似公式とその誤差について

Material type: 文書・図像類

Author: 藤田, 康介ほか

Publisher: 愛知工業大学

Publication date: 2001-03-31

Material Format: Digital

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Note (General)：: Let f(x) be continuous on the interval [a, b]. The mean value M(f) of f(x) on [a, b] is defined as follows : [numerical formula] where we denote by F(...

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Material Type: 文書・図像類
Title: 連続関数の平均値の近似公式とその誤差について
Author/Editor: 藤田, 康介
樋口, 功
Author Heading: 藤田, 康介
樋口, 功
Publication, Distribution, etc.: 愛知工業大学
Publication Date: 2001-03-31
Publication Date (W3CDTF): 2001-03-31
Alternative Title: Approximate Formula of Mean Value of Continuous Function and its Error Estimation
Periodical title: 愛知工業大学研究報告. A, 基礎教育センター論文集 = Bulletin of Aichi Institute of Technology. Part A
No. or year of volume/issue: 36
Volume: 36
Pages: 31-41
ISSN (Periodical Title): ISSN : 0387-0804
Text Language Code: jpn
Target Audience: 一般
Note (General): Let f(x) be continuous on the interval [a, b]. The mean value M(f) of f(x) on [a, b] is defined as follows : [numerical formula] where we denote by F(x) the primitive function of f(x). In the case when F(x) is unknown, we must calculate Ad (f) by the aid of so-called approximate formulas. In this paper, we shall obtain first an asymptotic expansion of the mean value M(f) with the terms of Riemann's quadrature by parts and next its end-points correction formula. We remark that the celebrated Euler-Maclaurin's summation formula is an immediate consequence of our asymptotic expansion just obtained. Further we shall derive some approximate formulas of mean value based on the function-values at random points.
identifier:http://repository.aitech.ac.jp/dspace/handle/11133/2014
Access Restrictions: 限定公開
Periodical Title (NCID): AA11564921
https://ci.nii.ac.jp/ncid/AA11564921
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