Massive 3-loop Ladder Diagrams for Quarkonic Local Operator Matrix   Elements
  3-loop diagrams of the ladder-type, which emerge for local quarkonic twist-2 operator matrix elements, are computed directly for general values of the Mellin variable $N$ using Appell-function representations and applying modern summation technologies provided by the package {\sf Sigma} and the method of hyperlogarithms. In some of the diagrams generalized harmonic sums with $\xi \in \{1,1/2,2\}$ emerge beyond the usual nested harmonic sums. As the asymptotic representation of the corresponding integrals shows, the generalized sums conspire giving well behaved expressions for large values of $N$. These diagrams contribute to the 3-loop heavy flavor Wilson coefficients of the structure functions in deep-inelastic scattering in the region $Q^2 \gg m^2$. 
Jakob Ablinger, Johannes Bl\"umlein, Alexander Hasselhuhn, Sebastian   Klein, Carsten Schneider, and Fabian Wi{\ss}brock
hep-ph hep-th math-ph math.MP