"Bailey lattice"의 두 판 사이의 차이

2020년 11월 16일 (월) 07:50 기준 최신판

non-unitary c(2,2k+1) minimal models

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-<h5 style="line-height: 3.428em; margin: 0px; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">introduction</h5>
+* [[non-unitary c(2,2k+1) minimal models]]
+[[분류:math and physics]]
-Let <math>\{\alpha_r\}, \{\beta_r\}</math> be a Bailey pair relative to a and set
+[[분류:migrate]]
-<math>\alpha_0'=\alpha_0</math>, <math>\alpha_n'=(1-a)a^nq^{n^2-n}(\frac{\alpha_n}{1-aq^{2n}}-\frac{aq^{2n-2}\alpha_{n-1}}{1-aq^{2n-2}})</math><math>\beta_n'=\sum_{r=0}^{n}\frac{a^rq^{r^2-r}}{(q)_{n-r}}\beta_{r}</math>
-Then <math>\{\alpha_r'\}, \{\beta_r'\}</math>  is a Bailey pair relative to <math>aq^{-1}</math>
-<h5 style="line-height: 2em; margin: 0px;">comparison with Bailey chain</h5>
-* [[6080259|Bailey chain]]<br><math>\alpha^\prime_n= a^nq^{n^2}\alpha_n</math><br><math>\beta^\prime_L = \sum_{r=0}^{L}\frac{a^rq^{r^2}}{(q)_{L-r}}\beta_r</math><br>
-*  This does not change the parameter a of the Bailey pair.<br>
-*  lattice construction changes this<br>
-<h5 style="line-height: 2em; margin: 0px;">corollary</h5>
-Let <math>\{\alpha_r\}, \{\beta_r\}</math> be the initial Bailey pair relative to a
-apply Bailey chain construction k-i-1 times ([[6080259|Bailey chain]])
-At the (k-i)th step apply Bailey lattice
-apply Bailey chain construction i times again.
-Then we get a Bailey pair
-<math>\{\alpha_r'\}, \{\beta_r'\}</math>  is a Bailey pair relative to <math>aq^{-1}</math>.
-If we use the defining relation of Bailey pair to <math>\{\alpha_r'\}, \{\beta_r'\}</math>,
-<math>\beta_L'=\sum_{r=0}^{L}\frac{\alpha_r'}{(q)_{L-r}(q)_{L+r}}</math>
-and take the limit L\to\infty
-<math>\sum_{n_1\geq\cdots\geq n_{k}\geq0}\frac{a^{n_1+\cdots+n_{k}}q^{n_1^2+\cdots+n_{k}^2}\beta_{n_{k}}}{(q)_{n_{1}-n_{2}}\cdots (q)_{n_{k-2}-n_{k-1}}(q)_{n_{k-1}-n_{k}}}=\frac{1}{(a)_{\infty}}\left{[}\alpha_0+(1-a)\sum_{n=1}^{\infty}(\frac{a^{kn}q^{kn^2-in}\alpha_n}{1-aq^{2n}}-\frac{a^{k(n-1)+i+1}q^{k(n-1)^2+(i+2)(n-1)}\alpha_{n-1}}{1-aq^{2n-2}})\right{]}</math>
-<h5 style="line-height: 2em; margin: 0px;">examples</h5>
-* [[Andrews-Gordon identity]]<br>
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-* http://www.google.com/search?hl=en&tbs=tl:1&q=
-<h5 style="line-height: 3.428em; margin: 0px; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">related items</h5>
-<h5 style="line-height: 3.428em; margin: 0px; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">encyclopedia</h5>
-* http://en.wikipedia.org/wiki/
-* http://www.scholarpedia.org/
-* Princeton companion to mathematics([[2910610/attachments/2250873|Companion_to_Mathematics.pdf]])
-<h5 style="line-height: 3.428em; margin: 0px; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">books</h5>
-* [[2010년 books and articles]]<br>
-* http://gigapedia.info/1/
-* http://gigapedia.info/1/
-* http://www.amazon.com/s/ref=nb_ss_gw?url=search-alias%3Dstripbooks&field-keywords=
-[[4909919|]]
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-* [http://www.liafa.jussieu.fr/%7Elovejoy/lattice.pdf A Bailey Lattice]<br>
-** Jeremy Lovejoy, Proceedings of the American Mathematical Society, Vol. 132, No. 5 (May, 2004), pp. 1507-1516
-*  The Bailey lattice<br>
-**  David Bressoud, an introduction, pp. 57--67 in Ramanujan Revisited. G. E. Andrews et al. eds., Academic Press, 1988.<br>
-*  The Bailey Lattice<br>
-**  A. Agarwal, G.E. Andrews, and D. Bressoud,  J. Indian Math. Soc. 51 (1987), 57-73.<br>
-* http://www.ams.org/mathscinet
-* [http://www.zentralblatt-math.org/zmath/en/ ]http://www.zentralblatt-math.org/zmath/en/
-* http://arxiv.org/
-* http://www.pdf-search.org/line-height: 2em;">
-* http://pythagoras0.springnote.com/
-* [http://math.berkeley.edu/%7Ereb/papers/index.html http://math.berkeley.edu/~reb/papers/index.html]
-* http://dx.doi.org/
-<h5 style="line-height: 3.428em; margin: 0px; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">question and answers(Math Overflow)</h5>
-* http://mathoverflow.net/search?q=
-* http://mathoverflow.net/search?q=
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-*  구글 블로그 검색<br>
-** http://blogsearch.google.com/blogsearch?q=
-** http://blogsearch.google.com/blogsearch?q=
-* http://ncatlab.org/nlab/show/HomePage
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-* http://arxiv.org/
-<h5 style="line-height: 3.428em; margin: 0px; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">links</h5>
-* [http://detexify.kirelabs.org/classify.html Detexify2 - LaTeX symbol classifier]
-* [http://pythagoras0.springnote.com/pages/1947378 수식표현 안내]
-* [http://www.research.att.com/%7Enjas/sequences/index.html The On-Line Encyclopedia of Integer Sequences]
-* http://functions.wolfram.com/
-*

"Bailey lattice"의 두 판 사이의 차이

2020년 11월 16일 (월) 07:50 기준 최신판

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