"Q-Chu-Vandermonde 항등식"의 두 판 사이의 차이
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(피타고라스님이 이 페이지의 위치를 <a href="/pages/4792049">양자미적분학(q-calculus)과 q-급수</a>페이지로 이동하였습니다.) |
Pythagoras0 (토론 | 기여) |
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| (사용자 2명의 중간 판 16개는 보이지 않습니다) | |||
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| − | + | ==개요== | |
| − | * [[ | + | * [[초기하급수의 합공식|초기하 급수의 합공식]] Chu-Vandermonde 공식:<math>\,_2F_1(-n,b;c;1)=\dfrac{(c-b)_{n}}{(c)_{n}}</math> |
| + | * q-analogue | ||
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<math> _2\phi_1(q^{-n},b;c;q,cq^n/b)=\frac{(cq^n;q)_\infty(c/b;q)_\infty}{(c;q)_\infty(cq^n/b;q)_\infty}=\frac{(c/b;q)_n}{(c;q)_n}</math> | <math> _2\phi_1(q^{-n},b;c;q,cq^n/b)=\frac{(cq^n;q)_\infty(c/b;q)_\infty}{(c;q)_\infty(cq^n/b;q)_\infty}=\frac{(c/b;q)_n}{(c;q)_n}</math> | ||
| 18번째 줄: | 10번째 줄: | ||
<math>_2\phi_1(q^{-n},b;c;q,q)=\frac{(c/b;q)_n}{(c;q)_n}b^n</math> | <math>_2\phi_1(q^{-n},b;c;q,q)=\frac{(c/b;q)_n}{(c;q)_n}b^n</math> | ||
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| − | + | ==메모== | |
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| − | + | ==관련된 항목들== | |
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| − | + | ==수학용어번역== | |
| − | * 단어사전 | + | * 단어사전 |
** http://www.google.com/dictionary?langpair=en|ko&q= | ** http://www.google.com/dictionary?langpair=en|ko&q= | ||
** http://ko.wiktionary.org/wiki/ | ** http://ko.wiktionary.org/wiki/ | ||
| − | * | + | * 발음사전 http://www.forvo.com/search/ |
| − | * [http://mathnet.kaist.ac.kr/mathnet/math_list.php?mode=list&ftype=&fstr= 대한수학회 수학 학술 용어집] | + | * [http://mathnet.kaist.ac.kr/mathnet/math_list.php?mode=list&ftype=&fstr= 대한수학회 수학 학술 용어집] |
** http://mathnet.kaist.ac.kr/mathnet/math_list.php?mode=list&ftype=eng_term&fstr= | ** http://mathnet.kaist.ac.kr/mathnet/math_list.php?mode=list&ftype=eng_term&fstr= | ||
* [http://www.nktech.net/science/term/term_l.jsp?l_mode=cate&s_code_cd=MA 남·북한수학용어비교] | * [http://www.nktech.net/science/term/term_l.jsp?l_mode=cate&s_code_cd=MA 남·북한수학용어비교] | ||
| − | * [http://kms.or.kr/home/kor/board/bulletin_list_subject.asp?bulletinid=%7BD6048897-56F9-43D7-8BB6-50B362D1243A%7D&boardname=%BC%F6%C7%D0%BF%EB%BE%EE%C5%E4%B7%D0%B9%E6&globalmenu=7&localmenu=4 | + | * [http://kms.or.kr/home/kor/board/bulletin_list_subject.asp?bulletinid=%7BD6048897-56F9-43D7-8BB6-50B362D1243A%7D&boardname=%BC%F6%C7%D0%BF%EB%BE%EE%C5%E4%B7%D0%B9%E6&globalmenu=7&localmenu=4 대한수학회 수학용어한글화 게시판] |
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| − | + | ==사전 형태의 자료== | |
* http://en.wikipedia.org/wiki/Q-Vandermonde_identity | * http://en.wikipedia.org/wiki/Q-Vandermonde_identity | ||
| 85번째 줄: | 53번째 줄: | ||
* [http://eqworld.ipmnet.ru/ The World of Mathematical Equations] | * [http://eqworld.ipmnet.ru/ The World of Mathematical Equations] | ||
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| − | + | ==리뷰논문과 에세이== | |
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| − | + | ==관련논문== | |
| − | * [http://dx.doi.org/10.1016/0012-365X%2884%2990149-3 Some generalized Durfee square identities] | + | * [http://dx.doi.org/10.1016/0012-365X%2884%2990149-3 Some generalized Durfee square identities] |
| − | ** Ira M. Gessel, | + | ** Ira M. Gessel, Discrete MathematicsVolume 49, Issue 1, March 1984, Pages 41-44 |
| − | * [http://dx.doi.org/10.1016/S0096-3003%2896%2900054-9 Some combinatorial identities associated with the Vandermonde convolution] | + | * [http://dx.doi.org/10.1016/S0096-3003%2896%2900054-9 Some combinatorial identities associated with the Vandermonde convolution] |
| − | ** H. W. Gould | + | ** H. W. Gould and H. M. Srivastava, 1997 |
| − | * [http://www.jstor.org/stable/2306429 Some Generalizations of Vandermonde's Convolution] | + | * [http://www.jstor.org/stable/2306429 Some Generalizations of Vandermonde's Convolution] |
| − | ** H. W. Gould, | + | ** H. W. Gould, The American Mathematical Monthly, Vol. 63, No. 2 (Feb., 1956), pp. 84-91 |
* http://www.jstor.org/action/doBasicSearch?Query= | * http://www.jstor.org/action/doBasicSearch?Query= | ||
| 108번째 줄: | 76번째 줄: | ||
* http://dx.doi.org/ | * http://dx.doi.org/ | ||
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| − | + | ==링크== | |
* [http://www.ams.org/news/math-in-the-media/mathdigest-index Summaries of Media Coverage of Math] | * [http://www.ams.org/news/math-in-the-media/mathdigest-index Summaries of Media Coverage of Math] | ||
| − | * | + | [[분류:q-급수]] |
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| + | ==메타데이터== | ||
| + | ===위키데이터=== | ||
| + | * ID : [https://www.wikidata.org/wiki/Q7265292 Q7265292] | ||
| + | ===Spacy 패턴 목록=== | ||
| + | * [{'LOWER': 'q'}, {'OP': '*'}, {'LOWER': 'vandermonde'}, {'LEMMA': 'identity'}] | ||
2021년 2월 17일 (수) 04:51 기준 최신판
개요
- 초기하 급수의 합공식 Chu-Vandermonde 공식\[\,_2F_1(-n,b;c;1)=\dfrac{(c-b)_{n}}{(c)_{n}}\]
- q-analogue
\( _2\phi_1(q^{-n},b;c;q,cq^n/b)=\frac{(cq^n;q)_\infty(c/b;q)_\infty}{(c;q)_\infty(cq^n/b;q)_\infty}=\frac{(c/b;q)_n}{(c;q)_n}\)
\(_2\phi_1(q^{-n},b;c;q,q)=\frac{(c/b;q)_n}{(c;q)_n}b^n\)
메모
관련된 항목들
수학용어번역
사전 형태의 자료
- http://en.wikipedia.org/wiki/Q-Vandermonde_identity
- http://en.wikipedia.org/wiki/Vandermonde's_identity
- http://mathworld.wolfram.com/q-Chu-VandermondeIdentity.html
- http://en.wikipedia.org/wiki/
- The Online Encyclopaedia of Mathematics
- NIST Digital Library of Mathematical Functions
- The World of Mathematical Equations
리뷰논문과 에세이
관련논문
- Some generalized Durfee square identities
- Ira M. Gessel, Discrete MathematicsVolume 49, Issue 1, March 1984, Pages 41-44
- Some combinatorial identities associated with the Vandermonde convolution
- H. W. Gould and H. M. Srivastava, 1997
- Some Generalizations of Vandermonde's Convolution
- H. W. Gould, The American Mathematical Monthly, Vol. 63, No. 2 (Feb., 1956), pp. 84-91
링크
메타데이터
위키데이터
- ID : Q7265292
Spacy 패턴 목록
- [{'LOWER': 'q'}, {'OP': '*'}, {'LOWER': 'vandermonde'}, {'LEMMA': 'identity'}]