"Slater 92"의 두 판 사이의 차이
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+ | Note | ||
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+ | * [[twisted Chebyshev polynomials and dilogarithm identities|an explanation for dilogarithm ladder]]<br>[[twisted Chebyshev polynomials and dilogarithm identities|]]<br> | ||
+ | * Loxton & Lewin<br><math>x, -y, -z^{-1}</math>가 방정식 <math>x^3+3x^2-1=0</math>의 해라고 하자.<br><math>3L(x^3)-9L(x^2)-9L(x)+7L(1)=0</math><br><math>3L(y^6)-6L(y^3)-27L(y^2)+18L(y)+2L(1)=0</math><br><math>3L(z^6)-6L(z^3)-27L(z^2)+18L(z)-2L(1)=0</math><br> | ||
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+ | <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%;">type of identity</h5> | ||
* [[Slater list|Slater's list]] | * [[Slater list|Slater's list]] | ||
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2010년 7월 27일 (화) 05:36 판
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
\(\sum_{n=0}^{\infty}\frac{(q^3;q^3)_{n}q^{n(n+1)}}{ (q)_{n}(q;q^{2})_n(q^2;q^2)_{n}}=\frac{(q^{9};q^{27})_{\infty}(q^{18};q^{27})_{\infty}(q^{27};q^{27})_{\infty}}{(q)_{\infty}}\)
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