"폴리로그 함수(polylogarithm)"의 두 판 사이의 차이

2012년 5월 28일 (월) 16:50 판

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

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

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

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

@@ 30번째 줄: / 30번째 줄: @@
 <h5 style="line-height: 2em; margin: 0px;">로그함수</h5>
-* [[로그 함수]]<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>
@@ 57번째 줄: / 55번째 줄: @@
 * [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/~dma0hg/kyoto.pdf]
+* [http://www.maths.dur.ac.uk/%7Ed40ppt/pdf/John_Rhodes.pdf http://www.maths.dur.ac.uk/~d40ppt/pdf/John_Rhodes.pdf]
 *  Math Overflow<br>
 ** http://mathoverflow.net/search?q=