Skip to main content

Research Repository

Advanced Search

Functional equations for higher logarithms

Gangl, H.



Following earlier work by Abel and others, Kummer gave in 1840 functional equations for the polylogarithm function Li_m(z) up to m = 5, but no example for larger m was known until recently. We give the first genuine 2-variable functional equation for the 7-logarithm. We investigate and relate identities for the 3-logarithm given by Goncharov and Wojtkowiak and deduce a certain family of functional equations for the 4-logarithm.


Gangl, H. (2003). Functional equations for higher logarithms. Selecta Mathematica (New Series), 9(3), 361 - 377.

Journal Article Type Article
Publication Date 2003-09
Deposit Date Feb 15, 2008
Journal Selecta Mathematica (New Series)
Print ISSN 1022-1824
Electronic ISSN 1420-9020
Publisher Springer
Peer Reviewed Not Peer Reviewed
Volume 9
Issue 3
Pages 361 - 377
Keywords Polylogarithms, Functional equations, Algebraic K-theory.