Generalized single-valued hyperlogarithms

Abstract

Single-valued hyperlogarithms are generalized to include primitives of differential forms $\mathrm{d} z/(az\overline{z}+bz+c\overline{z}+d)$, $a,b,c,d\in\mathbb{C}$, where $\overline{z}$ is the complex conjugate of the variable $z\in\mathbb{C}$. The construction of these generalized single-valued hyperlogarithms (GSVHs) relies on a commutative hexagon which allows one to express primitives as anti-primitives. The article provides a proved constructive theory of GSVHs.