"폴리로그 함수(polylogarithm)"의 두 판 사이의 차이
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이 항목의 스프링노트 원문주소==
Pythagoras0 (토론 | 기여) 잔글 (찾아 바꾸기 – “<h5>” 문자열을 “==” 문자열로) |
Pythagoras0 (토론 | 기여) 잔글 (찾아 바꾸기 – “</h5>” 문자열을 “==” 문자열로) |
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* [[폴리로그 함수(polylogarithm)]]<br> | * [[폴리로그 함수(polylogarithm)]]<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%;">개요 | + | <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%;">개요== |
* [[다이로그 함수(dilogarithm)|다이로그 함수(dilogarithm )]] 의 일반화<br> | * [[다이로그 함수(dilogarithm)|다이로그 함수(dilogarithm )]] 의 일반화<br> | ||
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| − | <h5 style="line-height: 2em; margin: 0px;">정의 | + | <h5 style="line-height: 2em; margin: 0px;">정의== |
<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}_r(z)= \sum_{n=1}^\infty {z^n \over n^r}=\int_0^z \operatorname{Li}_{r-1}(t) \frac{dt}{t}</math> | ||
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| − | <h5 style="line-height: 2em; margin: 0px;">로그함수 | + | <h5 style="line-height: 2em; margin: 0px;">로그함수== |
* [[로그 함수]]<br><math>-\log (1-z)=z+\frac{z^2}{2}+\frac{z^3}{3}+\frac{z^4}{4}+\frac{z^5}{5}+\cdots</math><br> | * [[로그 함수]]<br><math>-\log (1-z)=z+\frac{z^2}{2}+\frac{z^3}{3}+\frac{z^4}{4}+\frac{z^5}{5}+\cdots</math><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%;">역사 | + | <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%;">역사== |
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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 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== |
* http://mathoverflow.net/questions/25428/what-is-special-about-polylogarithms-that-leads-to-so-many-interesting-identities<br> | * http://mathoverflow.net/questions/25428/what-is-special-about-polylogarithms-that-leads-to-so-many-interesting-identities<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%;">관련된 항목들 | + | <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%;">관련된 항목들== |
* [[L-함수의 값 구하기 입문]]<br> | * [[L-함수의 값 구하기 입문]]<br> | ||
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* 단어사전 http://www.google.com/dictionary?langpair=en|ko&q= | * 단어사전 http://www.google.com/dictionary?langpair=en|ko&q= | ||
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* http://ko.wikipedia.org/wiki/ | * http://ko.wikipedia.org/wiki/ | ||
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| − | ==리뷰논문, 에세이, 강의노트 | + | ==리뷰논문, 에세이, 강의노트== |
* John R. Rhodes [http://www.mathematik.hu-berlin.de/%7Ekreimer/Polylogarithms.pdf Polylogarithms] ,2008 | * John R. Rhodes [http://www.mathematik.hu-berlin.de/%7Ekreimer/Polylogarithms.pdf Polylogarithms] ,2008 | ||
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* <br> | * <br> | ||
2012년 11월 1일 (목) 13:14 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==
- 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