Slater 92

Note

• an explanation for dilogarithm ladder
  [[twisted Chebyshev polynomials and dilogarithm identities|]]
  
• Loxton & Lewin
  \(x, -y, -z^{-1}\)가 방정식 \(x^3+3x^2-1=0\)의 해라고 하자.
  \(3L(x^3)-9L(x^2)-9L(x)+7L(1)=0\)
  \(3L(y^6)-6L(y^3)-27L(y^2)+18L(y)+2L(1)=0\)
  \(3L(z^6)-6L(z^3)-27L(z^2)+18L(z)-2L(1)=0\)
  

 

 

 

type of identity

• Slater's list
• B(3)
  
  

 

 

 

q-series identity

\(\sum_{n=0}^{\infty}\frac{(q^3;q^3)_{n}q^{n(n+1)}}{ (q)_{n}(q;q^{2})_n(q^2;q^2)_{n}}=\frac{(q^{9};q^{27})_{\infty}(q^{18};q^{27})_{\infty}(q^{27};q^{27})_{\infty}}{(q)_{\infty}}\)

 

• The On-Line Encyclopedia of Integer Sequences
  
  • http://www.research.att.com/~njas/sequences/?q=

 

 

 

Bethe type equation (cyclotomic equation)

\(\frac{(1-x)(1-x^2)^2}{(1-x^3)}=x^2\)

\(x^3+3x^2-1=0\)

\(x, -y, -z^{-1}\)가 방정식 의 해 http://www.wolframalpha.com/input/?i=x^3%2B3x^2-1%3D0

 

 

dilogarithm identity

\(L(x^3)-3L(x^2)-3L(x)=-\frac{7}{3}L(1)\)

 

 

 

 

 

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

 

• http://www.ams.org/mathscinet
• [1]http://www.zentralblatt-math.org/zmath/en/
• [2]http://arxiv.org/
• http://pythagoras0.springnote.com/
• http://math.berkeley.edu/~reb/papers/index.html
• http://dx.doi.org/