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    수학이 알고싶은 중고대딩들을 위한 수학 노트

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함수 다이로그 항등식(functional dilogarithm identity)

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이 항목의 수학노트 원문주소

 

 

개요

 

 

2항 관계식

S=\left\{x,\frac{1}{x}\right\}

\sum_{a\in S}L(\frac{1}{1+a})=L\left(\frac{1}{\frac{1}{x}+1}\right)+L\left(\frac{1}{x+1}\right)=L(1)

 

 

5항 관계식

S=\left\{x,y,\frac{x+1}{y},\frac{y+1}{x},\frac{x+y+1}{x y}\right\}

\sum_{a\in S}L(\frac{1}{1+a})=L\left(\frac{1}{\frac{x+1}{y}+1}\right)+L\left(\frac{1}{\frac{y+1}{x}+1}\right)+L\left(\frac{1}{\frac{x+y+1}{x y}+1}\right)+L\left(\frac{1}{x+1}\right)+L\left(\frac{1}{y+1}\right)=2L(1)

 

 

9항 관계식

\left\{x,y,z,\frac{x z+x+z+1}{y},\frac{x y+x z+x+y^2+y z+2 y+z+1}{x y z},\frac{x z+x+y+z+1}{x y},\frac{x z+x+y+z+1}{y z},\frac{y+1}{x},\frac{y+1}{z}\right\}

\sum_{a\in S}L(\frac{1}{1+a})=3L(1)

 

 

14항 관계식

\left\{x,z,\frac{(x+1) (z+1)}{y},\frac{z+1}{w},\frac{x z+x+y+z+1}{x y},\frac{(w+z+1) (x z+x+y+z+1)}{w y z},\frac{(y+z+1) (w (x+y+1)+x z+x+y+z+1)}{w x y z},

\left.\frac{w (x+y+1)+x z+x+y+z+1}{y z},\frac{w y+w+y+z+1}{w z},\frac{(x+y+1) (w y+w+y+z+1)}{x y z},\frac{(w+1) (y+1)}{z},\frac{y+1}{x},w,y\right\}

\sum_{a\in S}L(\frac{1}{1+a})=4L(1)

 

 

 

역사

 

 

 

메모

 

 

관련된 항목들

 

 

매스매티카 파일 및 계산 리소스

 

 

수학용어번역

 

 

 

사전 형태의 자료

 

 

리뷰논문, 에세이, 강의노트

 

 

관련논문

  • Chapoton, Frédéric. 2005. “Functional Identities for the Rogers Dilogarithm Associated to Cluster Y-Systems.” Bulletin of the London Mathematical Society 37 (5) (October 1): 755 -760. doi:10.1112/S0024609305004510.

  • Algebraic Dilogarithm Identities ,Basil Gordon  and Richard J. Mcintosh, 1997
  • L.J. Rogers, On Function Sum Theorems Connected with the Series Formula Proc. London Math. Soc. (1907) s2-4(1): 169-189 doi:10.1112/plms/s2-4.1.169
  • http://www.jstor.org/action/doBasicSearch?Query=
  • http://www.ams.org/mathscinet
  • http://dx.doi.org/10.1112/plms/s2-4.1.169

 

 

관련도서

  • 도서내검색

    • http://books.google.com/books?q=
    • http://book.daum.net/search/contentSearch.do?query=

 

 

링크

History

Last edited on 12/09/2011 12:50 by 피타고라스

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