폴리로그 함수(polylogarithm)
이 항목의 스프링노트 원문주소==
개요==
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==
메모==
- 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
관련된 항목들==
수학용어번역==
사전 형태의 자료==
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
- 로그 함수
\(-\log (1-z)=z+\frac{z^2}{2}+\frac{z^3}{3}+\frac{z^4}{4}+\frac{z^5}{5}+\cdots\)
- 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
-
- 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