"적분의 주제들"의 두 판 사이의 차이
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| 39번째 줄: | 39번째 줄: | ||
* [[로그 사인 적분 (log sine integrals)]] | * [[로그 사인 적분 (log sine integrals)]] | ||
| − | * [[로그 탄젠트 적분(log tangent integral)]] | + | * [[로그 탄젠트 적분(log tangent integral)]]<br><math>\int_{\pi/4}^{\pi/2} \ln \ln \tan x\, dx=\frac{\pi}{2}\ln{\frac{\Gamma(\frac{3}{4})}{\Gamma(\frac{1}{4})}\sqrt{2\pi}</math><br> |
| + | * [[다이로그 함수(dilogarithm)|다이로그 함수(dilogarithm )]]<br><math>\int_{0}^{\infty}\ln(1+e^{-x})}\,dx=\frac{\pi^2}{12}</math><br> | ||
| 106번째 줄: | 107번째 줄: | ||
* http://integrals.wolfram.com/index.jsp | * http://integrals.wolfram.com/index.jsp | ||
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| 111번째 줄: | 114번째 줄: | ||
<h5>관련논문</h5> | <h5>관련논문</h5> | ||
| − | * | + | * [http://www.ams.org/notices/201004/rtx100400476p.pdf Seized Opportunities]<br> |
| − | ** | + | ** Victor H. Moll, Notices of the AMS, Apr. 2010 |
| + | * [http://www.springerlink.com/content/wql8d40h20jljxp2/ On Some Integrals Involving the Hurwitz Zeta Function: Part 1]<br> | ||
| + | ** Olivier Espinosa and Victor H. Moll | ||
| + | * [http://www.springerlink.com/content/t285842772wv0767/ On Some Integrals Involving the Hurwitz Zeta Function: Part 2]<br> | ||
| + | ** Olivier Espinosa and Victor H. Moll | ||
* [http://www.math.tulane.edu/%7Evhm/papers_html/fea-moll.pdf The Evaluation of Integrals: A Personal Story]<br> | * [http://www.math.tulane.edu/%7Evhm/papers_html/fea-moll.pdf The Evaluation of Integrals: A Personal Story]<br> | ||
** Victor Moll, Notices Amer. Math. Soc. 49(3) (2002) 311-317 | ** Victor Moll, Notices Amer. Math. Soc. 49(3) (2002) 311-317 | ||
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* [http://www.jstor.org/stable/2325128 The Evolution of Integration]<br> | * [http://www.jstor.org/stable/2325128 The Evolution of Integration]<br> | ||
** A. Shenitzer and J. Steprans, The American Mathematical Monthly, Vol. 101, No. 1 (Jan., 1994), pp. 66-72 | ** A. Shenitzer and J. Steprans, The American Mathematical Monthly, Vol. 101, No. 1 (Jan., 1994), pp. 66-72 | ||
2010년 6월 18일 (금) 10:37 판
이 항목의 스프링노트 원문주소
개요
관련된 학부 과목과 미리 알고 있으면 좋은 것들
부정적분의 기술
정적분의 계산
- 로그 사인 적분 (log sine integrals)
- 로그 탄젠트 적분(log tangent integral)
\(\int_{\pi/4}^{\pi/2} \ln \ln \tan x\, dx=\frac{\pi}{2}\ln{\frac{\Gamma(\frac{3}{4})}{\Gamma(\frac{1}{4})}\sqrt{2\pi}\) - 다이로그 함수(dilogarithm )
\(\int_{0}^{\infty}\ln(1+e^{-x})}\,dx=\frac{\pi^2}{12}\)
Gradshteyn and Ryzhik
- http://www.math.tulane.edu/~vhm/Table.html
- Directory of notes on the integrals in GR
- http://arxiv.org/find/math/1/au:+Moll_V/0/1/0/all/0/1
- The integrals in Gradshteyn and Ryzhik. Part 1: A family of logarithmic integrals.
- Victor H. Moll
- Victor H. Moll
메모
관련된 대학원 과목
- differential Galois theory
관련된 항목들
관련도서
- Handbook of Integration
- Daniel Zwillinger, 1992
- Irresistible Integrals: Symbolics, Analysis and Experiments in the Evaluation of Integrals
- George Boros and Victor Moll, 2004
- http://www.amazon.com/s/ref=nb_ss_gw?url=search-alias%3Dstripbooks&field-keywords=Galois'
위키링크
관련웹페이지
관련논문
- Seized Opportunities
- Victor H. Moll, Notices of the AMS, Apr. 2010
- On Some Integrals Involving the Hurwitz Zeta Function: Part 1
- Olivier Espinosa and Victor H. Moll
- On Some Integrals Involving the Hurwitz Zeta Function: Part 2
- Olivier Espinosa and Victor H. Moll
- The Evaluation of Integrals: A Personal Story
- Victor Moll, Notices Amer. Math. Soc. 49(3) (2002) 311-317
- The Evolution of Integration
- A. Shenitzer and J. Steprans, The American Mathematical Monthly, Vol. 101, No. 1 (Jan., 1994), pp. 66-72
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