"로저스 다이로그 함수 (Rogers dilogarithm)"의 두 판 사이의 차이

2009년 12월 20일 (일) 13:13 판

\(x\in (0,1)\)에서 로저스 dilogarithm을 다음과 같이 정의
\(L(x)=\operatorname{Li}_2(x)+\frac{1}{2}\log x\log (1-x)=-\frac{1}{2}\int_{0}^{x}\frac{\log(1-y)}{y}+\frac{\log(1-y)}{1-y}dy\)
\((-\infty,0],[1,\+\infty)\)를 제외한 복소평면으로 해석적확장됨

\(L(0)=0\)

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

\(L(x)+L(1-x)=L(1)\)

\(L(x)+L(y)=L(xy)+L(\frac{x(1-y)}{1-xy})+L\Left( \frac{y(1-x)}{1-xy} )\right)\)

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 * [http://dx.doi.org/10.1023/A:1009709927327 Algebraic Dilogarithm Identities]<br>
 ** Basil Gordon  and Richard J. Mcintosh, 1997
+* [http://dx.doi.org/10.1143/PTPS.118.61 Dilogarithm identities]<br>
+** Anatol N. Kirillov,Prog.Theor.Phys.Suppl.118:61-142, 1995
 * [http://dx.doi.org/10.1007/BF01840426 Identities for the Rogers dilogarithm function connected with simple Lie algebras]<br>
 ** A. N. Kirillov
@@ 123번째 줄: / 125번째 줄: @@
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