"중심이항계수 (central binomial coefficient)"의 두 판 사이의 차이
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| 74번째 줄: | 74번째 줄: | ||
* [[카탈란 수열(Catalan numbers)]]<br> | * [[카탈란 수열(Catalan numbers)]]<br> | ||
* [[ζ(3)는 무리수이다(아페리의 정리)]]<br> | * [[ζ(3)는 무리수이다(아페리의 정리)]]<br> | ||
| + | * [[폴리로그 함수(polylogarithm)]]<br> | ||
| 115번째 줄: | 116번째 줄: | ||
* [http://arxiv.org/abs/hep-th/0004153 Central Binomial Sums, Multiple Clausen Values and Zeta Values]<br> | * [http://arxiv.org/abs/hep-th/0004153 Central Binomial Sums, Multiple Clausen Values and Zeta Values]<br> | ||
** J. M. Borwein, D. J. Broadhurst, J. Kamnitzer, 2000 | ** J. M. Borwein, D. J. Broadhurst, J. Kamnitzer, 2000 | ||
| + | * Interesting Series Involving the Central Binomial Coefficient<br> | ||
| + | * | ||
| + | * D. H. Lehmer, The American Mathematical Monthly, Vol. 92, No. 7 (Aug. - Sep., 1985), pp. 449-457 | ||
* [http://dx.doi.org/10.1016/0022-314X(85)90019-8 On the series Σk = 1∞(k2k)−1 k−n and related sums]<br> | * [http://dx.doi.org/10.1016/0022-314X(85)90019-8 On the series Σk = 1∞(k2k)−1 k−n and related sums]<br> | ||
** I. J. Zucker, Journal of Number Theory, Volume 20, Issue 1, February 1985, Pages 92-102 | ** I. J. Zucker, Journal of Number Theory, Volume 20, Issue 1, February 1985, Pages 92-102 | ||
| + | * Some wonderful formulas ... an introduction to polylogarithms<br> | ||
| + | ** A.J. Van der Poorten, Queen's papers in Pure and Applied Mathematics, 54 (1979), 269-286 | ||
* http://www.jstor.org/action/doBasicSearch?Query= | * http://www.jstor.org/action/doBasicSearch?Query= | ||
2010년 6월 8일 (화) 14:11 판
이 항목의 스프링노트 원문주소
개요
- 다음과 같은 이항계수로 정의
\({2n \choose n}=\frac{(2n)!}{(n!)^2}\)
Central Binomial Sums
역삼각함수
\(2(\sin^{-1} x)^2=\sum_{n=1}^{\finfty}\frac{(2x)^{2n}}{n^2\binom{2n}{n}}\)
리만제타함수
\(\zeta(2)=3\sum_{n=1}^{\infty}\frac{1}{n^{2}\binom{2n}{n}}\)
\(\zeta(3) = \frac{5}{2} \sum_{n=1}^\infty \frac{(-1)^{n-1}}{n^3\binom{2n}{n}}\)
\(\zeta(4) = \frac{36}{17} \sum_{n=1}^\infty \frac{1}{n^4\binom{2n}{n}}\)
재미있는 사실
- Math Overflow http://mathoverflow.net/search?q=
- 네이버 지식인 http://kin.search.naver.com/search.naver?where=kin_qna&query=
역사
메모
관련된 항목들
수학용어번역
- 단어사전 http://www.google.com/dictionary?langpair=en%7Cko&q=
- 발음사전 http://www.forvo.com/search/
- 대한수학회 수학 학술 용어집
- 남·북한수학용어비교
- 대한수학회 수학용어한글화 게시판
사전 형태의 자료
- http://ko.wikipedia.org/wiki/
- http://en.wikipedia.org/wiki/Central_binomial_coefficient
- http://mathworld.wolfram.com/CentralBinomialCoefficient.html
- http://mathworld.wolfram.com/BinomialSums.html
- http://www.wolframalpha.com/input/?i=
- NIST Digital Library of Mathematical Functions
- The On-Line Encyclopedia of Integer Sequences
관련논문
- Experimental Determination of Apéry-like Identities for ζ(2n + 2)
- David H. Bailey, Jonathan M. Borwein, and David M. Bradley
- Evaluations of binomial series
- Jonathan M. Borwein1 and Roland Girgensohn, 2004
- Central Binomial Sums, Multiple Clausen Values and Zeta Values
- J. M. Borwein, D. J. Broadhurst, J. Kamnitzer, 2000
- Interesting Series Involving the Central Binomial Coefficient
- D. H. Lehmer, The American Mathematical Monthly, Vol. 92, No. 7 (Aug. - Sep., 1985), pp. 449-457
- On the series Σk = 1∞(k2k)−1 k−n and related sums
- I. J. Zucker, Journal of Number Theory, Volume 20, Issue 1, February 1985, Pages 92-102
- Some wonderful formulas ... an introduction to polylogarithms
- A.J. Van der Poorten, Queen's papers in Pure and Applied Mathematics, 54 (1979), 269-286
관련도서
- 도서내검색
- 도서검색
관련기사
- 네이버 뉴스 검색 (키워드 수정)