"라마누잔-셀베르그 연분수"의 두 판 사이의 차이

@@ 1번째 줄: / 1번째 줄: @@
-<h5 style="background-position: 0px 100%; font-size: 1.16em; margin: 0px; color: rgb(34, 61, 103); line-height: 3.42em; font-family: 'malgun gothic',dotum,gulim,sans-serif;">introduction</h5>
-* [[octahedron and modular functions|octahedron]]<br>
-* '''[Duke2005] '''(9.1)<br><math>u(\tau)={\sqrt{2}q^{1/8} \over 1+ } {q \over 1+q+} {q^2 \over 1+q^2+} {q^3 \over 1+q^3} \cdots=\sqrt{2}q^{1/8}\prod_{n=1}^{\infty}(1+q^{n})^{(-1)^{n}}=\sqrt{2}q^{1/8}\frac{(-q^{2};q^{2})_{\infty}} {(-q;q^{2})_{\infty}}</math><br><math>v(\tau)={q^{1/2} \over 1+q + } {q \over 1+q^2+} {q^2 \over 1+q^3} } \cdots=q^{1/2}\prod_{n=1}^{\infty}(1-q^{n})^{(\frac{8}{n})}=q^{1/2}\frac{(q^{1};q^{8})_{\infty}(q^{7};q^{8})_{\infty}}{(q^{3};q^{8})_{\infty}(q^{5};q^{8})_{\infty}}</math><br>
-*  Selberg continued fractions '''[Duke2005] '''(9.13, 155p)<br><math>S_1(q)=\sqrt{2}q^{1/8}\frac{(-q^{2};q^{2})_{\infty}} {(-q;q^{2})_{\infty}}=u(\tau)=\sqrt{2}\frac{\eta(\tau)\eta^{2}(4\tau)}{\eta^{3}(2\tau)}</math><br><math>S_2(q)=q^{1/8}\frac{(-q^{2};q^{2})_{\infty}} {(q;q^{2})_{\infty}}=q^{1/8}\frac{(-q^{2};q^{2})_{\infty}(q^2;q^{2})_{\infty}}{(q;q^{2})_{\infty}(q^2;q^{2})_{\infty}} =\frac{\eta(4\tau)}{\eta(\tau)}</math><br> S1 and S2 are notations from '''[Chan2009]'''<br>
-* [http://pythagoras0.springnote.com/pages/12510508 q-series 의 공식 모음]
-<h5 style="margin: 0px; line-height: 2em;">relation with other modular functions</h5>
-<h5 style="background-position: 0px 100%; font-size: 1.16em; margin: 0px; color: rgb(34, 61, 103); line-height: 3.42em; font-family: 'malgun gothic',dotum,gulim,sans-serif;">history</h5>
-* http://www.google.com/search?hl=en&tbs=tl:1&q=
-<h5 style="background-position: 0px 100%; font-size: 1.16em; margin: 0px; color: rgb(34, 61, 103); line-height: 3.42em; font-family: 'malgun gothic',dotum,gulim,sans-serif;">related items</h5>
-* [[Weber functions and conformal field theory]]<br>
-<h5 style="background-position: 0px 100%; font-size: 1.16em; margin: 0px; color: rgb(34, 61, 103); line-height: 3.42em; font-family: 'malgun gothic',dotum,gulim,sans-serif;">encyclopedia</h5>
-* http://en.wikipedia.org/wiki/
-* http://www.scholarpedia.org/
-* Princeton companion to mathematics([[2910610/attachments/2250873|Companion_to_Mathematics.pdf]])
-<h5 style="background-position: 0px 100%; font-size: 1.16em; margin: 0px; color: rgb(34, 61, 103); line-height: 3.42em; font-family: 'malgun gothic',dotum,gulim,sans-serif;">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|]]
-<h5 style="background-position: 0px 100%; font-size: 1.16em; margin: 0px; color: rgb(34, 61, 103); line-height: 3.42em; font-family: 'malgun gothic',dotum,gulim,sans-serif;">articles</h5>
-* [http://dx.doi.org/0.1090/S0002-9939-09-09835-9 From a Ramanujan-Selberg continued fraction to a Jacobian identity]<br>
-**  Hei-Chi ChanJournal: Proc. Amer. Math. Soc. 137 (2009), 2849-2856.<br>
-* [http://dx.doi.org/10.1155/IJMMS/2006/54901 Modular relations and explicit values of Ramanujan-Selberg continued fractions]<br>
-**  Nayandeep Deka Baruah and Nipen Saikia, 2006<br>
-* [http://www.ams.org/proc/2002-130-01/S0002-9939-01-06183-4/home.html Explicit evaluations of a Ramanujan-Selberg continued fraction]<br>
-**  Liang-Cheng Zhang, 2002<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/
-* http://pythagoras0.springnote.com/
-* [http://math.berkeley.edu/%7Ereb/papers/index.html http://math.berkeley.edu/~reb/papers/index.html]
-* http://dx.doi.org/10.1090/S0002-9947-02-03155-0
-<h5 style="background-position: 0px 100%; font-size: 1.16em; margin: 0px; color: rgb(34, 61, 103); line-height: 3.42em; font-family: 'malgun gothic',dotum,gulim,sans-serif;">question and answers(Math Overflow)</h5>
-* http://mathoverflow.net/search?q=
-* http://mathoverflow.net/search?q=
-<h5 style="background-position: 0px 100%; font-size: 1.16em; margin: 0px; color: rgb(34, 61, 103); line-height: 3.42em; font-family: 'malgun gothic',dotum,gulim,sans-serif;">blogs</h5>
-*  구글 블로그 검색<br>
-** http://blogsearch.google.com/blogsearch?q=
-** http://blogsearch.google.com/blogsearch?q=
-* http://ncatlab.org/nlab/show/HomePage
-<h5 style="background-position: 0px 100%; font-size: 1.16em; margin: 0px; color: rgb(34, 61, 103); line-height: 3.42em; font-family: 'malgun gothic',dotum,gulim,sans-serif;">experts on the field</h5>
-* http://arxiv.org/
-<h5 style="background-position: 0px 100%; font-size: 1.16em; margin: 0px; color: rgb(34, 61, 103); line-height: 3.42em; font-family: 'malgun gothic',dotum,gulim,sans-serif;">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/
-*

"라마누잔-셀베르그 연분수"의 두 판 사이의 차이

2012년 7월 24일 (화) 08:49 판

둘러보기 메뉴

검색