"Bailey pair and lemma"의 두 판 사이의 차이
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<h5 style="line-height: 2em; margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; color: rgb(34, 61, 103); font-family: 'malgun gothic', dotum, gulim, sans-serif; font-size: 1.166em; background-image: ; background-color: initial; background-position: 0px 100%;">Bailey lemma</h5> | <h5 style="line-height: 2em; margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; color: rgb(34, 61, 103); font-family: 'malgun gothic', dotum, gulim, sans-serif; font-size: 1.166em; background-image: ; background-color: initial; background-position: 0px 100%;">Bailey lemma</h5> | ||
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| + | <h5 style="line-height: 2em; margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px;">Bailey chain</h5> | ||
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| + | * we derive a new Bailey chain from a known Bailey pair<br><math>\alpha^\prime_n= \frac{(\rho_1;q)_n(\rho_2;q)_n(aq/\rho_1\rho_2)^n\alpha_n}{(aq/\rho_1;q)_n(aq/\rho_2;q)_n}</math><br><math>\beta^\prime_n = \sum_{j\ge0}\frac{(\rho_1;q)_j(\rho_2;q)_j(aq/\rho_1\rho_2;q)_{n-j}(aq/\rho_1\rho_2)^j\beta_j}{(q;q)_{n-j}(aq/\rho_1;q)_n(aq/\rho_2;q)_n}</math><br> | ||
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* [http://arxiv.org/abs/0910.2062v2 50 Years of Bailey's lemma]<br> | * [http://arxiv.org/abs/0910.2062v2 50 Years of Bailey's lemma]<br> | ||
** S. Ole Warnaar, 2009<br> | ** S. Ole Warnaar, 2009<br> | ||
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* [http://www.springerlink.com/content/478544t414l26v05/ Andrews–Gordon type identities from combinations of Virasoro characters]<br> | * [http://www.springerlink.com/content/478544t414l26v05/ Andrews–Gordon type identities from combinations of Virasoro characters]<br> | ||
** Boris Feigin, Omar Foda, Trevor Welsh, 2007<br> | ** Boris Feigin, Omar Foda, Trevor Welsh, 2007<br> | ||
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* [http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.10.5670 Finite Rogers-Ramanujan Type Identities]<br> | * [http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.10.5670 Finite Rogers-Ramanujan Type Identities]<br> | ||
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* Andrew V. Sills, 2003<br> | * Andrew V. Sills, 2003<br> | ||
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* [http://www.combinatorics.org/Surveys/ds15.pdf Rogers-Ramanujan-Slater Type identities]<br> | * [http://www.combinatorics.org/Surveys/ds15.pdf Rogers-Ramanujan-Slater Type identities]<br> | ||
** Mc Laughlin<br> | ** Mc Laughlin<br> | ||
* [http://dx.doi.org/10.1142/S0217751X97001110 Virasoro character identities from the Andrews–Bailey construction]<br> | * [http://dx.doi.org/10.1142/S0217751X97001110 Virasoro character identities from the Andrews–Bailey construction]<br> | ||
** Foda, O., Quano, Y.-H, Int. J. Mod. Phys. A 12, 1651–1675 (1997)<br> | ** Foda, O., Quano, Y.-H, Int. J. Mod. Phys. A 12, 1651–1675 (1997)<br> | ||
| + | * [http://dx.doi.org/10.1112%2Fplms%2Fs2-54.2.147 Further identities of the Rogers-Ramanujan type]<br> | ||
| + | ** Slater, L. J. (1952), Proceedings of the London Mathematical Society. Second Series 54: 147–167<br> | ||
* http://www.ams.org/mathscinet | * http://www.ams.org/mathscinet | ||
2010년 6월 10일 (목) 06:41 판
introduction
Bailey lemma
Bailey pair
- the sequence \(\{\alpha_r\}, \{\beta_r\}\) satisfying the following is called a Bailey pair
\(\beta_L=\sum_{r=0}^{L}\frac{\alpha_r}{(q)_{L-r}(aq)_{L+r}}\) - conjugate Bailey pair \(\{\delta_r\}, \{\gamma_r\}\)
\(\gamma_L=\sum_{r=L}^{\infty}\frac{\delta_r}{(q)_{r-L}(aq)_{r+L}}\)
Bailey chain
- we derive a new Bailey chain from a known Bailey pair
\(\alpha^\prime_n= \frac{(\rho_1;q)_n(\rho_2;q)_n(aq/\rho_1\rho_2)^n\alpha_n}{(aq/\rho_1;q)_n(aq/\rho_2;q)_n}\)
\(\beta^\prime_n = \sum_{j\ge0}\frac{(\rho_1;q)_j(\rho_2;q)_j(aq/\rho_1\rho_2;q)_{n-j}(aq/\rho_1\rho_2)^j\beta_j}{(q;q)_{n-j}(aq/\rho_1;q)_n(aq/\rho_2;q)_n}\)
history
encyclopedia
- http://en.wikipedia.org/wiki/Bailey_pair
- http://en.wikipedia.org/wiki/
- http://www.scholarpedia.org/
- Princeton companion to mathematics(Companion_to_Mathematics.pdf)
books
- 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
- 50 Years of Bailey's lemma
- S. Ole Warnaar, 2009
- S. Ole Warnaar, 2009
- Andrews–Gordon type identities from combinations of Virasoro characters
- Boris Feigin, Omar Foda, Trevor Welsh, 2007
- Boris Feigin, Omar Foda, Trevor Welsh, 2007
- Finite Rogers-Ramanujan Type Identities
- Andrew V. Sills, 2003
- Rogers-Ramanujan-Slater Type identities
- Mc Laughlin
- Mc Laughlin
- Virasoro character identities from the Andrews–Bailey construction
- Foda, O., Quano, Y.-H, Int. J. Mod. Phys. A 12, 1651–1675 (1997)
- Foda, O., Quano, Y.-H, Int. J. Mod. Phys. A 12, 1651–1675 (1997)
- Further identities of the Rogers-Ramanujan type
- Slater, L. J. (1952), Proceedings of the London Mathematical Society. Second Series 54: 147–167
- Slater, L. J. (1952), Proceedings of the London Mathematical Society. Second Series 54: 147–167
- http://www.ams.org/mathscinet
- http://www.zentralblatt-math.org/zmath/en/
- http://pythagoras0.springnote.com/
- http://math.berkeley.edu/~reb/papers/index.html[1]
- http://front.math.ucdavis.edu/search?a=&t=&c=&n=40&s=Listings&q=
- http://www.ams.org/mathscinet/search/publications.html?pg4=AUCN&s4=&co4=AND&pg5=TI&s5=&co5=AND&pg6=PC&s6=&co6=AND&pg7=ALLF&co7=AND&Submit=Search&dr=all&yrop=eq&arg3=&yearRangeFirst=&yearRangeSecond=&pg8=ET&s8=All&s7=
- http://dx.doi.org/
question and answers(Math Overflow)
blogs
experts on the field