"폴리로그 함수(polylogarithm)"의 두 판 사이의 차이
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<h5 style="line-height: 2em; margin: 0px;">정의</h5> | <h5 style="line-height: 2em; margin: 0px;">정의</h5> | ||
| − | + | <math>\operatorname{Li}_r(z)= \sum_{n=1}^\infty {z^n \over n^r}=\int_0^z \operatorname{Li}_{r-1}(t) \frac{dt}{t}</math> | |
| − | <math>\operatorname{Li} | + | <math>\operatorname{Li}_3(z) =\int_0^z \operatorname{Li}_2(t) \frac{dt}{t}</math> |
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| − | + | <h5 style="line-height: 2em; margin: 0px;">로그함수</h5> | |
| − | < | + | * [[로그 함수]]<br> |
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<h5 style="line-height: 3.428em; margin: 0px; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">메모</h5> | <h5 style="line-height: 3.428em; margin: 0px; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">메모</h5> | ||
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| + | * http://mathoverflow.net/questions/25428/what-is-special-about-polylogarithms-that-leads-to-so-many-interesting-identities<br> | ||
* 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 | * 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 | ||
* [http://www.maths.dur.ac.uk/%7Edma0hg/kyoto.pdf Functional equations of polylogarithms] Herbert Gangl<br> | * [http://www.maths.dur.ac.uk/%7Edma0hg/kyoto.pdf Functional equations of polylogarithms] Herbert Gangl<br> | ||
| − | * '[http://www.maths.dur.ac.uk/%7Edma0hg/kyoto.pdf | + | * '[http://www.maths.dur.ac.uk/%7Edma0hg/kyoto.pdf http://www.maths.dur.ac.uk/~dma0hg/kyoto.pdf] |
| + | * Math Overflow<br> | ||
| + | ** http://mathoverflow.net/search?q= | ||
2012년 5월 28일 (월) 08:32 판
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
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
- Math Overflow
관련된 항목들
수학용어번역
- 단어사전 http://www.google.com/dictionary?langpair=en%7Cko&q=
- 발음사전 http://www.forvo.com/search/
- 대한수학회 수학 학술 용어집
- 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
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