Geodesic
Clean Single-Valued Polylogarithms
Symmetry, integrability and geometry: methods and applications, Tome 17 (2021) Cet article a éte moissonné depuis la source Math-Net.Ru

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We define a variant of real-analytic polylogarithms that are single-valued and that satisfy “clean” functional relations that do not involve any products of lower weight functions. We discuss the basic properties of these functions and, for depths one and two, we present some explicit formulas and results. We also give explicit formulas for the single-valued and clean single-valued version attached to the Nielsen polylogarithms $S_{n,2}(x)$, and we show how the clean single-valued functions give new evaluations of multiple polylogarithms at certain algebraic points.
Keywords: Hopf algebras, Dynkin operator, functional equations, single-valued projection, special values.
Mots-clés : multiple polylogarithms, Nielsen polylogarithms 
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     author = {Steven Charlton and Claude Duhr and Herbert Gangl},
     title = {Clean {Single-Valued} {Polylogarithms}},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2021_17_a106/}
}
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Steven Charlton; Claude Duhr; Herbert Gangl. Clean Single-Valued Polylogarithms. Symmetry, integrability and geometry: methods and applications, Tome 17 (2021). http://geodesic.mathdoc.fr/item/SIGMA_2021_17_a106/

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