Graphical functions in parametric space
arXiv:1509.07296 · doi:10.1007/s11005-016-0935-6
Abstract
Graphical functions are positive functions on the punctured complex plane which arise in quantum field theory. We generalize a parametric integral representation for graphical functions due to Lam, Lebrun and Nakanishi, which implies the real analyticity of graphical functions. Moreover we prove a formula that relates graphical functions of planar dual graphs.
v2: extended introduction, minor changes in notation and correction of misprints