"다이로그 항등식 (dilogarithm identities)"의 두 판 사이의 차이

2010년 2월 9일 (화) 13:42 판

로저스 dilogarithm \(L(x)\)
dilogarithm 항등식
대수적수 \(x_i\)와 유리수 \(c\)에 대한 다음과 같은 형태의 항등식
\(\sum_{i=1}^{N}L(x_i)=cL(1)\)
Polylogarithm ladders 으로 불리기도 한다다

\(L(1)=\frac{\pi^2}{6}\)

\(-2L(-1)=L(1)\)

\(2L(\frac{1}{2})=L(1)\)

\(5L(\frac{3-\sqrt{5}}{2})=2L(1)\)

\(5L(\frac{-1+\sqrt{5}}{2})=3L(1)\)

\(\rho=\tfrac{1}{2}(\sqrt{5}-1)\) 는 황금비

\(L(\rho^6)=4L(\rho^3)+3L(\rho^2)-6L(\rho)+\frac{7\pi^2}{30}\)

\(L(\rho^{12})=2L(\rho^6)+3L(\rho^4)+4L(\rho^3)-6L(\rho^2)+\frac{7\pi^2}{10}\)

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 <h5 style="line-height: 2em; margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px;">콕세터(1935)</h5>
+<math>\rho=\tfrac{1}{2}(\sqrt{5}-1)</math> 는 [[황금비]]
 <math>L(\rho^6)=4L(\rho^3)+3L(\rho^2)-6L(\rho)+\frac{7\pi^2}{30}</math>
+<math>L(\rho^{12})=2L(\rho^6)+3L(\rho^4)+4L(\rho^3)-6L(\rho^2)+\frac{7\pi^2}{10}</math>
+<math>L(\rho^{12})=2L(\rho^6)+3L(\rho^4)+4L(\rho^3)-6L(\rho^2)+\frac{7\pi^2}{10}</math>
@@ 116번째 줄: / 126번째 줄: @@
 * [http://dx.doi.org/10.1143/PTPS.118.61 Dilogarithm identities]<br>
 ** Anatol N. Kirillov,Prog.Theor.Phys.Suppl.118:61-142, 1995
-* The functions of Schlafli and Lobatschefsky".
+* [http://dx.doi.org/10.1093/qmath/os-6.1.13 The functions of Schlafli and Lobatschefsky]<br>
-* Quarterly Journal of Mathematics (Oxford) 6: 13–29. doi:10.1093/qmath/os-6.1.13
+** Coxeter, H.S.M. (1935),  Quarterly Journal of Mathematics (Oxford) 6: 13–29. doi:
 * http://www.jstor.org/action/doBasicSearch?Query=
 * http://www.ams.org/mathscinet
-* http://dx.doi.org/
+* http://dx.doi.org/10.1093/qmath/os-6.1.13