폴리로그 함수(polylogarithm)

이 항목의 스프링노트 원문주소

• 폴리로그 함수(polylogarithm)
  

 

 

개요

• 다이로그 함수(dilogarithm ) 의 일반화
  
• http://www.ega-math.narod.ru/Apery2.htm
  

 

 

 

정의

\(\operatorname{Li}_r(z)= \sum_{n=1}^\infty {z^n \over n^r}=\int_0^z \operatorname{Li}_{r-1}(t) \frac{dt}{t}\)

\(\operatorname{Li}_3(z) =\int_0^z \operatorname{Li}_2(t) \frac{dt}{t}\)

 

 

로그함수

• 로그 함수
  \(-\log (1-z)=z+\frac{z^2}{2}+\frac{z^3}{3}+\frac{z^4}{4}+\frac{z^5}{5}+\cdots\)
  

 

 

역사

 

• http://www.google.com/search?hl=en&tbs=tl:1&q=
• 수학사연표
•  

 

 

메모

• http://mathoverflow.net/questions/25428/what-is-special-about-polylogarithms-that-leads-to-so-many-interesting-identities
  

• http://books.google.com/books?hl=ko&lr=&id=9G3nlZUDAhkC&oi=fnd&pg=PA391&dq=The+classical+polylogarithms,+algebraic+K-theory&ots=zst2m387di&sig=kNRuqZp_mUdFDXScW41qNbprgps#v=onepage&q=&f=false
• Functional equations of polylogarithms Herbert Gangl
  
• http://www.maths.dur.ac.uk/~dma0hg/kyoto.pdf
• http://www.maths.dur.ac.uk/~d40ppt/pdf/John_Rhodes.pdf
• Math Overflow
  
  • http://mathoverflow.net/search?q=

 

 

관련된 항목들

• L-함수의 값 구하기 입문
  
• 파이에 대한 BBP 공식
  
• 로그 사인 적분 (log sine integrals)
  

 

 

수학용어번역

• 단어사전 http://www.google.com/dictionary?langpair=en%7Cko&q=
• 발음사전 http://www.forvo.com/search/
• 대한수학회 수학 학술 용어집
  
  • http://mathnet.kaist.ac.kr/mathnet/math_list.php?mode=list&ftype=eng_term&fstr=
• 남·북한수학용어비교
• 대한수학회 수학용어한글화 게시판

 

 

사전 형태의 자료

• http://ko.wikipedia.org/wiki/
• http://en.wikipedia.org/wiki/Polylogarithm
• http://en.wikipedia.org/wiki/
• http://www.wolframalpha.com/input/?i=
• NIST Digital Library of Mathematical Functions
• The On-Line Encyclopedia of Integer Sequences
  
  • http://www.research.att.com/~njas/sequences/?q=

 

 

리뷰논문, 에세이, 강의노트

• John R. Rhodes Polylogarithms ,2008
• Richard Hain, Classical Polylogarithms , 1992

 

 

 

관련논문

•  
  
• Multiple Polylogarithms: A Brief Survey Douglas Bowman, David M. Bradley, 5 Oct 2003
  
• Polylogarithmic ladders, hypergeometric series and the ten millionth digits of $\zeta(3)$ and $\zeta(5)$ D. J. Broadhurst, 1998
  
• On the rapid computation of various polylogarithmic constants David Bailey; Peter Borwein; Simon Plouffe.Journal: Math. Comp. 66 (1997), 903-913.
  
• Ramakrishnan, Analogs of the Bloch-Wigner function for higher polylogarithms, 1986
  
• The classical polylogarithms, algebraic K-theory and ζ. F. (n), Goncharov, A. Proc. of the Gelfand Seminar, Birkhauser, 113-135
  
• Some wonderful formulas ... an introduction to polylogarithms A.J. Van der Poorten, Queen's papers in Pure and Applied Mathematics, 54 (1979), 269-286 (http://www.ega-math.narod.ru/Apery2.htm )
  
• http://www.jstor.org/action/doBasicSearch?Query=polylogarithm
• http://www.jstor.org/action/doBasicSearch?Query=
• http://www.ams.org/mathscinet
• http://dx.doi.org/http://dx.doi.org/10.1090%2FS0025-5718-97-00856-9