Structural Relations between Nested Harmonic Sums

We describe the structural relations between nested harmonic sums emerging in the description of physical single scale quantities up to the 3–loop level in renormalizable gauge field theories. These are weight w=6 harmonic sums. We identify universal basic functions which allow to describe a large class of physical quantities and derive their complex analysis. For the 3–loop QCD Wilson coefficients 35 basic functions are required, whereas a subset of 15 describes the 3–loop anomalous dimensions.