Geodesic
Identities for Generalized Polylogarithms
Matematičeskie zametki, Tome 73 (2003) no. 4, pp. 613-624 
E. A. Ulanskii. Identities for Generalized Polylogarithms. Matematičeskie zametki, Tome 73 (2003) no. 4, pp. 613-624. http://geodesic.mathdoc.fr/item/MZM_2003_73_4_a12/
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     author = {E. A. Ulanskii},
     title = {Identities for {Generalized} {Polylogarithms}},
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     volume = {73},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2003_73_4_a12/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

We study the behavior of generalized polylogarithms under the action of the group of fractional-linear transformations of the argument. This group is formed by the transformations $z\mapsto1-z$ and $z\mapsto-z/(1-z)$, the last of which allows us to obtain identities of the form $$ \operatorname{Li}_k\biggl(\frac{-z}{1-z}\biggr) =-\sum_{|\bar s|=k}\operatorname{Li}_{\bar s}(z). $$ We prove that these identities imply the linear independence of generalized polylogarithms and the algebraic independence of classical polylogarithms over the field $\mathbb C(z)$.

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