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.

35 pages

References in corpus (3)

• Algorithms for the symbolic integration of hyperlogarithms with applications to Feynman integrals
• Numbers and Functions in Quantum Field Theory
• Graphical functions in even dimensions

Cited by in corpus (2)

• Five loop renormalization of ${\varphi }^3$ theory with applications to the Lee-Yang edge singularity and percolation theory
• Graphical functions in even dimensions