Ramanujan's Cubic Continued fractions
imported>Pythagoras0님의 2012년 10월 28일 (일) 15:38 판 (찾아 바꾸기 – “</h5>” 문자열을 “==” 문자열로)
introduction== \({1 \over 1+} {q+q^2 \over 1+} {q^{2}+a^{4} \over 1+} {q^3+q^6 \over 1+}{\cdots} =\frac{(q;q^{2})_{\infty}}{(q^{3};q^{6})^{3}_{\infty}}\) \(\frac{q^{1/3}}{1} {\ \atop+} \frac{q+q^2}{1}{\ \atop+} \frac{q^2+q^4}{1} {\ \atop+\dots}=q^{1/3}\frac{(q;q^{2})_{\infty}}{(q^{3};q^{6})^{3}_{\infty}} \) \(\frac{\Gamma(\frac{1}{6})\Gamma(\frac{3}{6})\Gamma(\frac{5}{6})}{\Gamma(\frac{3}{6})^{3}}=2\)
history== \(G(q)= \frac{q^{1/3}}{1} {\ \atop+} \frac{q+q^2}{1}{\ \atop+} \frac{q^2+q^4}{1} {\ \atop+\dots} \quad |q|<1\)
related items==
encyclopedia==
- 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==
- 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)
- Theorems Stated by Ramanujan (IX): Two Continued Fractions.
- Watson, G. N. 1929
Ramanujan's class invariants and cubic continued fraction
Berndt, 1995
- http://www.ams.org/mathscinet
- [1]http://www.zentralblatt-math.org/zmath/en/
- http://arxiv.org/
- http://www.pdf-search.org/
- http://pythagoras0.springnote.com/
- http://math.berkeley.edu/~reb/papers/index.html
- http://dx.doi.org/
http://www.emis.de/journals/ETNA/vol.25.2006/pp158-165.dir/pp158-165.pdf
[2]
- Chan, H.-C, 2010
- C. Adiga, T. Kim, M.S.Mahadeva Naika, H. S. Madhusudhan, 2005
- Bhargava, S., Vasuki, K.R., Sreeramamurthy, T.G., Indian J. Pure Appl. Math. 35, 1003–1025 (2004)
- Chan, H.-C, Int. J. Number Theory
- Heng Huat Chan, ACTA ARITHMETICA. LXXIII.4 (1995)
- Watson, G. N. 1929