"앤드류스-고든 항등식(Andrews-Gordon identity)"의 두 판 사이의 차이
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* [[앤드류스-고든 항등식(Andrews-Gordon identity)]]<br> | * [[앤드류스-고든 항등식(Andrews-Gordon identity)]]<br> | ||
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* [[로저스-라마누잔 항등식|로저스-라마누잔 연분수와 항등식]]의 일반화<br> | * [[로저스-라마누잔 항등식|로저스-라마누잔 연분수와 항등식]]의 일반화<br> | ||
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<math>\sum_{n_1,\cdots,n_{k-1}\geq0}\frac{x^{N_1^2+\cdots+N_{k-1}^2+N_i+\cdots+N_{k-1}}}{(x)_{n_1}...(x)_{n_{k-1}}}=\prod_{r\neq 0,\pm i \pmod {2k+1}}\frac{1}{1-x^r} </math> | <math>\sum_{n_1,\cdots,n_{k-1}\geq0}\frac{x^{N_1^2+\cdots+N_{k-1}^2+N_i+\cdots+N_{k-1}}}{(x)_{n_1}...(x)_{n_{k-1}}}=\prod_{r\neq 0,\pm i \pmod {2k+1}}\frac{1}{1-x^r} </math> | ||
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| − | <h5 style="line-height: 2em; margin | + | <h5 style="line-height: 2em; margin: 0px;">얻어지는 이차형식</h5> |
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* 1961 고든<br> | * 1961 고든<br> | ||
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* 단어사전 http://www.google.com/dictionary?langpair=en|ko&q= | * 단어사전 http://www.google.com/dictionary?langpair=en|ko&q= | ||
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* http://ko.wikipedia.org/wiki/ | * http://ko.wikipedia.org/wiki/ | ||
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* http://www.wolframalpha.com/input/?i= | * http://www.wolframalpha.com/input/?i= | ||
* [http://dlmf.nist.gov/ NIST Digital Library of Mathematical Functions] | * [http://dlmf.nist.gov/ NIST Digital Library of Mathematical Functions] | ||
| − | * [http://www.research.att.com/ | + | * [http://www.research.att.com/%7Enjas/sequences/index.html The On-Line Encyclopedia of Integer Sequences]<br> |
** http://www.research.att.com/~njas/sequences/?q= | ** http://www.research.att.com/~njas/sequences/?q= | ||
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* [http://dx.doi.org/10.1007/s11139-006-0150-7 The Rogers–Selberg recursions, the Gordon–Andrews identities and intertwining operators]<br> | * [http://dx.doi.org/10.1007/s11139-006-0150-7 The Rogers–Selberg recursions, the Gordon–Andrews identities and intertwining operators]<br> | ||
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* [http://www.math.psu.edu/andrews/pdf/58.pdf On the General Rogers-Ramanujan Theorem.]<br> | * [http://www.math.psu.edu/andrews/pdf/58.pdf On the General Rogers-Ramanujan Theorem.]<br> | ||
** Andrews, G. E. Providence, RI: Amer. Math. Soc., 1974.<br> | ** Andrews, G. E. Providence, RI: Amer. Math. Soc., 1974.<br> | ||
| − | * | + | * [http://www.pnas.org/content/71/10/4082.short An Analytic Generalization of the Rogers-Ramanujan Identities for Odd Moduli]<br> |
** George E. Andrews, PNAS October 1, 1974 vol. 71 no. 10 4082-4085<br> | ** George E. Andrews, PNAS October 1, 1974 vol. 71 no. 10 4082-4085<br> | ||
* [http://www.jstor.org/stable/2372962 A Combinatorial Generalization of the Rogers-Ramanujan Identities]<br> | * [http://www.jstor.org/stable/2372962 A Combinatorial Generalization of the Rogers-Ramanujan Identities]<br> | ||
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* 도서내검색<br> | * 도서내검색<br> | ||
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* 네이버 뉴스 검색 (키워드 수정)<br> | * 네이버 뉴스 검색 (키워드 수정)<br> | ||
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* 구글 블로그 검색<br> | * 구글 블로그 검색<br> | ||
2010년 10월 5일 (화) 18:22 판
이 항목의 스프링노트 원문주소
개요
- 로저스-라마누잔 연분수와 항등식의 일반화
항등식
\(\sum_{n_1,\cdots,n_{k-1}\geq0}\frac{x^{N_1^2+\cdots+N_{k-1}^2+N_i+\cdots+N_{k-1}}}{(x)_{n_1}...(x)_{n_{k-1}}}=\prod_{r\neq 0,\pm i \pmod {2k+1}}\frac{1}{1-x^r} \)
이 때, \(N_j=n_j+\cdots+n_{k-1}\)
얻어지는 이차형식
\(n_{1}^{2}\)
\((n_{1}+n_{2})^{2}+n_{2}^{2}\)
\((n_{1}+n_{2}+n_{3})^{2}+(n_{2}+n_{3})^{2}+n_{3}^{2}\)
\((n_{1}+n_{2}+n_{3}+n_{4})^{2}+(n_{2}+n_{3}+n_{4})^{2}+(n_{3}+n_{4})^{2}+n_{4}^{2}\)
행렬은
\(\text{A=}\left( \begin{array}{ccccc} 2 & 2 & 2 & 2 & 2 \\ 2 & 4 & 4 & 4 & 4 \\ 2 & 4 & 6 & 6 & 6 \\ 2 & 4 & 6 & 8 & 8 \\ 2 & 4 & 6 & 8 & 10 \end{array} \right)\)
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/
- http://www.proofwiki.org/wiki/
- http://mathworld.wolfram.com/Andrews-GordonIdentity.html
- http://www.wolframalpha.com/input/?i=
- NIST Digital Library of Mathematical Functions
- The On-Line Encyclopedia of Integer Sequences
관련논문
- The Rogers–Selberg recursions, the Gordon–Andrews identities and intertwining operators
- Stefano Capparelli, James Lepowsky, Antun Milas, 2004
- Some formulas related to dilogarithms, the zeta function and the Andrews–Gordon identities
- B. Richmond and G. Szekeres, 1981
- A general theory of identities of the Rogers-Ramanujan type
- George E. Andrews, Bull. Amer. Math. Soc. Volume 80, Number 6 (1974), 1033-1052.
- On the General Rogers-Ramanujan Theorem.
- Andrews, G. E. Providence, RI: Amer. Math. Soc., 1974.
- Andrews, G. E. Providence, RI: Amer. Math. Soc., 1974.
- An Analytic Generalization of the Rogers-Ramanujan Identities for Odd Moduli
- George E. Andrews, PNAS October 1, 1974 vol. 71 no. 10 4082-4085
- George E. Andrews, PNAS October 1, 1974 vol. 71 no. 10 4082-4085
- A Combinatorial Generalization of the Rogers-Ramanujan Identities
- Gordon, B. Amer. J. Math. 83, 393-399, 1961.
- Gordon, B. Amer. J. Math. 83, 393-399, 1961.
관련도서
- 도서내검색
- 도서검색
관련기사
- 네이버 뉴스 검색 (키워드 수정)