"Q-analogue of summation formulas"의 두 판 사이의 차이
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* [http://pythagoras0.springnote.com/pages/5980283 초기하 급수의 합공식]<br> | * [http://pythagoras0.springnote.com/pages/5980283 초기하 급수의 합공식]<br> | ||
| + | * q-Chu-Vandermonde<br><math>_2\phi_1(q^{-n},b;c;q,q)=\frac{(c/b;q)_n}{(c;q)_n}b^n</math><br> | ||
* '''[GR2004]''' (1.5.1) Heine's q-analogue of Gauss' summation formula<br><math>_2\phi_1(a,b;c,q,c/ab)=\frac{(c/a;q)_{\infty}(c/b;q)_{\infty}}{(c;q)_{\infty}(c/(ab);q)_{\infty}}</math> or <br><math>\sum_{n=0}^{\infty}\frac{(a,q)_{n}(b,q)_{n}}{(c ,q)_{n}(q ,q)_{n}}(\frac{c}{ab})^{n}=\frac{(c/a;q)_{\infty}(c/b;q)_{\infty}}{(c;q)_{\infty}(c/(ab);q)_{\infty}}</math><br> | * '''[GR2004]''' (1.5.1) Heine's q-analogue of Gauss' summation formula<br><math>_2\phi_1(a,b;c,q,c/ab)=\frac{(c/a;q)_{\infty}(c/b;q)_{\infty}}{(c;q)_{\infty}(c/(ab);q)_{\infty}}</math> or <br><math>\sum_{n=0}^{\infty}\frac{(a,q)_{n}(b,q)_{n}}{(c ,q)_{n}(q ,q)_{n}}(\frac{c}{ab})^{n}=\frac{(c/a;q)_{\infty}(c/b;q)_{\infty}}{(c;q)_{\infty}(c/(ab);q)_{\infty}}</math><br> | ||
* '''[GR2004]''' (1.7.2) q-analogue of Pfaff-Saalschutz's summation formula<br><math>_3\phi_2(a,b,q^{-n};c,abc^{-1}q^{1-n};q,q)=\frac{(c/a,c/b;q)_{n}}{(c,c/ab;q)_{n}}</math> or<br><math>\sum_{n=0}^{\infty}\frac{(a,q)_{n}(b,q)_{n}(q^{-n},q)_{n}}{(c)_{n}(abc^{-1}q^{1-n} ,q)_{n}(q ,q)_{n}}q^{n}=\frac{(c/a,c/b;q)_{n}}{(c,c/ab;q)_{n}}</math><br> | * '''[GR2004]''' (1.7.2) q-analogue of Pfaff-Saalschutz's summation formula<br><math>_3\phi_2(a,b,q^{-n};c,abc^{-1}q^{1-n};q,q)=\frac{(c/a,c/b;q)_{n}}{(c,c/ab;q)_{n}}</math> or<br><math>\sum_{n=0}^{\infty}\frac{(a,q)_{n}(b,q)_{n}(q^{-n},q)_{n}}{(c)_{n}(abc^{-1}q^{1-n} ,q)_{n}(q ,q)_{n}}q^{n}=\frac{(c/a,c/b;q)_{n}}{(c,c/ab;q)_{n}}</math><br> | ||
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* http://www.google.com/search?hl=en&tbs=tl:1&q= | * http://www.google.com/search?hl=en&tbs=tl:1&q= | ||
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* http://en.wikipedia.org/wiki/ | * http://en.wikipedia.org/wiki/ | ||
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* '''[GR2004]'''[http://books.google.com/books?id=31l4uC7lqGAC&dq=Gasper,+George;+Rahman,+Mizan+%282004%29,+Basic+hypergeometric+series Basic hypergeometric series]<br> | * '''[GR2004]'''[http://books.google.com/books?id=31l4uC7lqGAC&dq=Gasper,+George;+Rahman,+Mizan+%282004%29,+Basic+hypergeometric+series Basic hypergeometric series]<br> | ||
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* [http://arxiv.org/ ]http://arxiv.org/ | * [http://arxiv.org/ ]http://arxiv.org/ | ||
* http://pythagoras0.springnote.com/ | * http://pythagoras0.springnote.com/ | ||
| − | * http://math.berkeley.edu/~reb/papers/index.html | + | * [http://math.berkeley.edu/%7Ereb/papers/index.html http://math.berkeley.edu/~reb/papers/index.html] |
* http://dx.doi.org/ | * http://dx.doi.org/ | ||
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* http://mathoverflow.net/search?q= | * http://mathoverflow.net/search?q= | ||
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* 구글 블로그 검색<br> | * 구글 블로그 검색<br> | ||
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* http://arxiv.org/ | * http://arxiv.org/ | ||
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* [http://detexify.kirelabs.org/classify.html Detexify2 - LaTeX symbol classifier] | * [http://detexify.kirelabs.org/classify.html Detexify2 - LaTeX symbol classifier] | ||
* [http://pythagoras0.springnote.com/pages/1947378 수식표현 안내] | * [http://pythagoras0.springnote.com/pages/1947378 수식표현 안내] | ||
| − | * [http://www.research.att.com/ | + | * [http://www.research.att.com/%7Enjas/sequences/index.html The On-Line Encyclopedia of Integer Sequences] |
* http://functions.wolfram.com/ | * http://functions.wolfram.com/ | ||
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2011년 6월 19일 (일) 04:58 판
introduction
- 초기하 급수의 합공식
- q-Chu-Vandermonde
\(_2\phi_1(q^{-n},b;c;q,q)=\frac{(c/b;q)_n}{(c;q)_n}b^n\) - [GR2004] (1.5.1) Heine's q-analogue of Gauss' summation formula
\(_2\phi_1(a,b;c,q,c/ab)=\frac{(c/a;q)_{\infty}(c/b;q)_{\infty}}{(c;q)_{\infty}(c/(ab);q)_{\infty}}\) or
\(\sum_{n=0}^{\infty}\frac{(a,q)_{n}(b,q)_{n}}{(c ,q)_{n}(q ,q)_{n}}(\frac{c}{ab})^{n}=\frac{(c/a;q)_{\infty}(c/b;q)_{\infty}}{(c;q)_{\infty}(c/(ab);q)_{\infty}}\) - [GR2004] (1.7.2) q-analogue of Pfaff-Saalschutz's summation formula
\(_3\phi_2(a,b,q^{-n};c,abc^{-1}q^{1-n};q,q)=\frac{(c/a,c/b;q)_{n}}{(c,c/ab;q)_{n}}\) or
\(\sum_{n=0}^{\infty}\frac{(a,q)_{n}(b,q)_{n}(q^{-n},q)_{n}}{(c)_{n}(abc^{-1}q^{1-n} ,q)_{n}(q ,q)_{n}}q^{n}=\frac{(c/a,c/b;q)_{n}}{(c,c/ab;q)_{n}}\) - q-analogue of Whipple's theorem
- Jackson's q-analogue of Dougall's theorem
history
encyclopedia
- http://en.wikipedia.org/wiki/
- http://www.scholarpedia.org/
- Princeton companion to mathematics(Companion_to_Mathematics.pdf)
books
- [GR2004]Basic hypergeometric series
- Gasper, George; Rahman, Mizan (2004)
- 2010년 books and articles
- http://gigapedia.info/1/
- http://gigapedia.info/1/
- http://www.amazon.com/s/ref=nb_ss_gw?url=search-alias%3Dstripbooks&field-keywords=
[[4909919|]]
articles
- http://www.ams.org/mathscinet
- [1]http://www.zentralblatt-math.org/zmath/en/
- [2]http://arxiv.org/
- http://pythagoras0.springnote.com/
- http://math.berkeley.edu/~reb/papers/index.html
- http://dx.doi.org/
question and answers(Math Overflow)
blogs
experts on the field