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http://hdl.handle.net/11133/2014
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Title: | 連続関数の平均値の近似公式とその誤差について |
Other Titles: | Approximate Formula of Mean Value of Continuous Function and its Error Estimation |
Authors: | 藤田, 康介 樋口, 功 FUJITA, Kosuke HIGUCHI, Isao |
Issue Date: | 31-Mar-2001 |
Publisher: | 愛知工業大学 |
Abstract: | 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. |
URI: | http://hdl.handle.net/11133/2014 |
Appears in Collections: | 36号
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