"Ramanujan's Cubic Continued fractions"의 두 판 사이의 차이

2010년 7월 22일 (목) 04:43 판

introduction

\({1 \over 1+} {q+q^2 \over 1+} {q^{2}+a^{4} \over 1+} {q^3+q^6 \over 1+}{\cdots} =\frac{(q;q^{2})_{\infty}}{(q^{3};q^{6})^{3}_{\infty}}\)

\(\frac{q^{1/3}}{1} {\ \atop+} \frac{q+q^2}{1}{\ \atop+} \frac{q^2+q^4}{1} {\ \atop+\dots}=q^{1/3}\frac{(q;q^{2})_{\infty}}{(q^{3};q^{6})^{3}_{\infty}} \)

history

http://www.google.com/search?hl=en&tbs=tl:1&q=

related items

encyclopedia

http://en.wikipedia.org/wiki/
http://www.scholarpedia.org/
Princeton companion to mathematics(Companion_to_Mathematics.pdf)

books

[[4909919|]]

articles

A new proof of two identities involving Ramanujan’s cubic continued fraction
- Chan, H.-C, 2010
On Ramanujan's cubic continued fraction and explicit evaluations of theta-functions
- C. Adiga, T. Kim, M.S.Mahadeva Naika, H. S. Madhusudhan, 2005
Some evaluations of Ramanujan’s cubic continued fraction(http://www.zentralblatt-math.org/zmath/search/?an=1148.11303)
- Bhargava, S., Vasuki, K.R., Sreeramamurthy, T.G., Indian J. Pure Appl. Math. 35, 1003–1025 (2004)
Ramanujan's cubic continued fraction and Ramanujan type congruences for a certain partition function.
- Chan, H.-C, Int. J. Number Theory
On Ramanujan’s cubic continued fraction
- Heng Huat Chan, ACTA ARITHMETICA. LXXIII.4 (1995)

http://www.emis.de/journals/ETNA/vol.25.2006/pp158-165.dir/pp158-165.pdf

Ramanujan's class invariants and cubic continued fraction

Berndt, 1995

question and answers(Math Overflow)

blogs

구글 블로그 검색
- http://blogsearch.google.com/blogsearch?q=
- http://blogsearch.google.com/blogsearch?q=
http://ncatlab.org/nlab/show/HomePage

experts on the field

http://arxiv.org/

@@ 1번째 줄: / 1번째 줄: @@
 <h5 style="line-height: 3.428em; 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%;">introduction</h5>
-<math>{1 \over 1+} {q+q^2 \over 1+} {q^{2}+a^{4} \over 1+} {q^3+q^6 \over 1+}{\cdots} </math>
+<math>{1 \over 1+} {q+q^2 \over 1+} {q^{2}+a^{4} \over 1+} {q^3+q^6 \over 1+}{\cdots} =\frac{(q;q^{2})_{\infty}}{(q^{3};q^{6})^{3}_{\infty}}</math>
+<math>\frac{q^{1/3}}{1} {\ \atop+} \frac{q+q^2}{1}{\ \atop+} \frac{q^2+q^4}{1} {\ \atop+\dots}=q^{1/3}\frac{(q;q^{2})_{\infty}}{(q^{3};q^{6})^{3}_{\infty}} </math>
@@ 52번째 줄: / 54번째 줄: @@
 * [http://arxiv.org/abs/math/0502323 On Ramanujan's cubic continued fraction and explicit evaluations of theta-functions]<br>
 **  C. Adiga, T. Kim, M.S.Mahadeva Naika, H. S. Madhusudhan, 2005<br>
+*  Some evaluations of Ramanujan’s cubic continued fraction(http://www.zentralblatt-math.org/zmath/search/?an=1148.11303)<br>
+**  Bhargava, S., Vasuki, K.R., Sreeramamurthy, T.G., Indian J. Pure Appl. Math. 35, 1003–1025 (2004)<br>
 *  Ramanujan's cubic continued fraction and Ramanujan type congruences for a certain partition function.<br>
 **  Chan, H.-C,  Int. J. Number Theory<br>