폴리로그 함수(polylogarithm)

수학노트
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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

\[-\log (1-z)=z+\frac{z^2}{2}+\frac{z^3}{3}+\frac{z^4}{4}+\frac{z^5}{5}+\cdots\]



역사




메모

관련된 항목들



사전 형태의 자료


리뷰논문, 에세이, 강의노트

  • Vergu, C. “Polylogarithm Identities, Cluster Algebras and the N=4 Supersymmetric Theory.” arXiv:1512.08113 [hep-Th], December 26, 2015. http://arxiv.org/abs/1512.08113.
  • John R. Rhodes Polylogarithms ,2008
  • Bowman, Douglas, and David M. Bradley. “Multiple Polylogarithms: A Brief Survey.” arXiv:math/0310062, October 5, 2003. http://arxiv.org/abs/math/0310062.
  • Hain, Richard. “Classical Polylogarithms.” arXiv:alg-geom/9202022, February 20, 1992. http://arxiv.org/abs/alg-geom/9202022.
  • 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.
  • 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 )

관련논문