Numerical Evaluation of Goursat's Infinite Integral with an Unbounded Function

Material type: 文書・図像類

Author: HATANO, Yasuyoほか

Publisher: Springer Science + Business Media

Publication date: 2009-10

Material Format: Digital

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Note (General)：: The infinite integral R ∞ 0 xdx/(1+x^6 sin^2 x) converges but is hard to evaluate because the integrand f (x) = x/(1+x^6 sin^2 x) is a non-convergent ...

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Material Type: 文書・図像類
Title: Numerical Evaluation of Goursat's Infinite Integral with an Unbounded Function
Author/Editor: HATANO, Yasuyo
NINOMIYA, Ichizo
SUGIURA, Hiroshi
HASEGAWA, Takemitsu
Author Heading: HATANO, Yasuyo
NINOMIYA, Ichizo
SUGIURA, Hiroshi
HASEGAWA, Takemitsu
Publication, Distribution, etc.: Springer Science + Business Media
Publication Date: 2009-10
Publication Date (W3CDTF): 2009-10
Periodical title: Numerical Algorithms
No. or year of volume/issue: 52 2
Volume: 52
Issue: 2
Pages: 213-224
ISSN (Periodical Title): ISSN : 1017-1398
Text Language Code: eng
Subject Heading: Infinite integral
unbounded integrand
contour integral
residuals
numerical evaluation
high accuracy
octuple precision
Target Audience: 一般
Note (General): The infinite integral R ∞ 0 xdx/(1+x^6 sin^2 x) converges but is hard to evaluate because the integrand f (x) = x/(1+x^6 sin^2 x) is a non-convergent and unbounded function, indeed f (kπ) = kπ →∞ (k →∞). We show an efficient method to evaluate the above integral in high accuracy and actually obtain an approximate value in up to 73 significant digits on an octuple precision system in C++.
Source: https://u-fukui.repo.nii.ac.jp/?action=repository_action_common_download&item_id=22227&item_no=1&attribute_id=22&file_no=1
https://u-fukui.repo.nii.ac.jp/?action=repository_action_common_download&item_id=22227&item_no=1&attribute_id=22&file_no=1
Access Restrictions: 限定公開
Related Material: The original publication is available at www.springerlink.com
Related Material (DOI): 10.1007/s11075-009-9265-4
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): 福井大学 : 福井大学学術機関リポジトリ