"폴리로그 함수(polylogarithm)"의 두 판 사이의 차이
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Pythagoras0 (토론 | 기여) (→관련논문) |
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==관련논문== | ==관련논문== | ||
| + | * Rudenko, Daniil. “On the Functional Equations for Polylogarithms in One Variable.” arXiv:1511.09110 [math], November 2, 2015. http://arxiv.org/abs/1511.09110. | ||
* Sakugawa, Kenji, and Shin-ichiro Seki. “On Functional Equations of Finite Multiple Polylogarithms.” arXiv:1509.07653 [math], September 25, 2015. http://arxiv.org/abs/1509.07653. | * Sakugawa, Kenji, and Shin-ichiro Seki. “On Functional Equations of Finite Multiple Polylogarithms.” arXiv:1509.07653 [math], September 25, 2015. http://arxiv.org/abs/1509.07653. | ||
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* [http://arxiv.org/abs/math.CA/9803067 Polylogarithmic ladders, hypergeometric series and the ten millionth digits of $\zeta(3)$ and $\zeta(5)$] D. J. Broadhurst, 1998 | * [http://arxiv.org/abs/math.CA/9803067 Polylogarithmic ladders, hypergeometric series and the ten millionth digits of $\zeta(3)$ and $\zeta(5)$] D. J. Broadhurst, 1998 | ||
* [http://dx.doi.org/http://dx.doi.org/10.1090%2FS0025-5718-97-00856-9 On the rapid computation of various polylogarithmic constants] David Bailey; Peter Borwein; Simon Plouffe.Journal: Math. Comp. 66 (1997), 903-913. | * [http://dx.doi.org/http://dx.doi.org/10.1090%2FS0025-5718-97-00856-9 On the rapid computation of various polylogarithmic constants] David Bailey; Peter Borwein; Simon Plouffe.Journal: Math. Comp. 66 (1997), 903-913. | ||
2015년 12월 25일 (금) 03:13 판
개요
- 다이로그 함수(dilogarithm) 의 일반화
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
\[-\log (1-z)=z+\frac{z^2}{2}+\frac{z^3}{3}+\frac{z^4}{4}+\frac{z^5}{5}+\cdots\]
역사
메모
- Scheider, René. “The de Rham Realization of the Elliptic Polylogarithm in Families.” arXiv:1408.3819 [math], August 17, 2014. http://arxiv.org/abs/1408.3819.
- 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
관련된 항목들
사전 형태의 자료
리뷰논문, 에세이, 강의노트
- John R. Rhodes Polylogarithms ,2008
- Richard Hain, Classical Polylogarithms , 1992
- 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 )
- Askey, Richard. 1982. “Book Review: Polylogarithms and Associated Functions.” American Mathematical Society. Bulletin. New Series 6 (2): 248–251. doi:10.1090/S0273-0979-1982-14998-9.
관련논문
- Rudenko, Daniil. “On the Functional Equations for Polylogarithms in One Variable.” arXiv:1511.09110 [math], November 2, 2015. http://arxiv.org/abs/1511.09110.
- Sakugawa, Kenji, and Shin-ichiro Seki. “On Functional Equations of Finite Multiple Polylogarithms.” arXiv:1509.07653 [math], September 25, 2015. http://arxiv.org/abs/1509.07653.
- 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 $\zeta_F(n)$, Goncharov, A. Proc. of the Gelfand Seminar, Birkhauser, 113-135