"라마누잔과 파이"의 두 판 사이의 차이
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(피타고라스님이 이 페이지에 ramanujan_pi.nb 파일을 등록하셨습니다.) |
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<h5>참고할만한 자료</h5> | <h5>참고할만한 자료</h5> | ||
| + | * 공식을 구현한 매쓰매티카 파일<br> | ||
| + | ** [[3006616/attachments/1360956|ramanujan_pi.nb]] | ||
* [http://www.jstor.org/stable/2325206 Ramanujan, Modular Equations, and Approximations to Pi or How to Compute One Billion Digits of Pi]<br> | * [http://www.jstor.org/stable/2325206 Ramanujan, Modular Equations, and Approximations to Pi or How to Compute One Billion Digits of Pi]<br> | ||
** J. M. Borwein, P. B. Borwein and D. H. Bailey | ** J. M. Borwein, P. B. Borwein and D. H. Bailey | ||
** <cite>The American Mathematical Monthly</cite>, Vol. 96, No. 3 (Mar., 1989), pp. 201-219 | ** <cite>The American Mathematical Monthly</cite>, Vol. 96, No. 3 (Mar., 1989), pp. 201-219 | ||
| + | * Class number three Ramanujan type series for 1/tt<br> | ||
* [http://www.imsc.res.in/%7Erao/ramanujan/CamUnivCpapers/Cpaper6/page1.htm Modular equations and approximations to Pi]<br> | * [http://www.imsc.res.in/%7Erao/ramanujan/CamUnivCpapers/Cpaper6/page1.htm Modular equations and approximations to Pi]<br> | ||
** S. Ramanujan | ** S. Ramanujan | ||
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** Nayandeep Deka Baruaha, and Bruce C. Berndt | ** Nayandeep Deka Baruaha, and Bruce C. Berndt | ||
** Journal of Mathematical Analysis and Applications, Volume 341, Issue 1, 2007 | ** Journal of Mathematical Analysis and Applications, Volume 341, Issue 1, 2007 | ||
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| + | [http://ko.wikipedia.org/wiki/http://en.wikipedia.org/wiki/ ] | ||
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* http://ko.wikipedia.org/wiki/ | * http://ko.wikipedia.org/wiki/ | ||
* http://en.wikipedia.org/wiki/ | * http://en.wikipedia.org/wiki/ | ||
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네이버 뉴스 검색 (키워드 수정) | 네이버 뉴스 검색 (키워드 수정) | ||
| − | * http://news.search.naver.com/search.naver?where=news&x=0&y=0&sm=tab_hty&query= | + | * [http://news.search.naver.com/search.naver?where=news&x=0&y=0&sm=tab_hty&query=%EB%9D%BC%EB%A7%88%EB%88%84%EC%9E%94 http://news.search.naver.com/search.naver?where=news&x=0&y=0&sm=tab_hty&query=라마누잔] |
| − | * http://news.search.naver.com/search.naver?where=news&x=0&y=0&sm=tab_hty&query= | + | * [http://news.search.naver.com/search.naver?where=news&x=0&y=0&sm=tab_hty&query=%ED%8C%8C%EC%9D%B4 http://news.search.naver.com/search.naver?where=news&x=0&y=0&sm=tab_hty&query=파이] |
* http://news.search.naver.com/search.naver?where=news&x=0&y=0&sm=tab_hty&query= | * http://news.search.naver.com/search.naver?where=news&x=0&y=0&sm=tab_hty&query= | ||
* http://news.search.naver.com/search.naver?where=news&x=0&y=0&sm=tab_hty&query= | * http://news.search.naver.com/search.naver?where=news&x=0&y=0&sm=tab_hty&query= | ||
2009년 4월 4일 (토) 21:06 판
간단한 소개
- \(\frac{1}{\pi}= \frac{2\sqrt2}{9801}\sum_{n=0}^{\infty}\frac{(4n)!(1103+26390n)}{(n!)^{4}396^{4n}}\)
\[\frac{426880 \sqrt{10005}}{\pi} = \sum_{k=0}^\infty \frac{(6k)! (13591409 + 545140134k)}{(3k)!(k!)^3 (-640320)^{3k}}\!\]
하위주제들
하위페이지
재미있는 사실
관련된 단원
많이 나오는 질문
관련된 고교수학 또는 대학수학
관련된 다른 주제들
관련도서 및 추천도서
- Pi and the AGM
- Jonathan M. Borwein, Peter B. Borwein
- 도서내검색
- 도서검색
참고할만한 자료
- 공식을 구현한 매쓰매티카 파일
- Ramanujan, Modular Equations, and Approximations to Pi or How to Compute One Billion Digits of Pi
- J. M. Borwein, P. B. Borwein and D. H. Bailey
- The American Mathematical Monthly, Vol. 96, No. 3 (Mar., 1989), pp. 201-219
- Class number three Ramanujan type series for 1/tt
- Modular equations and approximations to Pi
- S. Ramanujan
- Quart. J. Pure Appl. Math., (1914), vol. 45, p. 350-372
- Approximations and complex multiplication according to Ramanujan
- D. V. Chudnovsky and G. V. Chudnovsky,
- Ramanujan Revisited, Academic Press Inc., Boston, (1988), p. 375-396 & p. 468-472.
- A WZ Proof of Ramanujan's Formula for Pi
- Shalosh B. Ekhad and Doron Zeilberger
- `Geometry, Analysis, and Mechanics', ed. by J.M. Rassias, World Scientific, Singapore, 1994, 107-108.
- Explicit Ramanujan-type approximations to pi of high order
- J. M. Borwein, P. B. Borwein
- 1987
- Ramanujan's series for 1/π arising from his cubic and quartic theories of elliptic functions
- Nayandeep Deka Baruaha, and Bruce C. Berndt
- Journal of Mathematical Analysis and Applications, Volume 341, Issue 1, 2007
관련기사
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