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We calculate convergent 3-loop Feynman diagrams containing a single massiveloop equipped with twist $\tau =2$ local operator insertions corresponding tospin $N$. They contribute to the massive operator matrix elements in QCDdescribing the massive Wilson coefficients for deep-inelastic scattering atlarge virtualities. Diagrams of this kind can be computed using an extendedversion to the method of hyperlogarithms, originally being designed formassless Feynman diagrams without operators. The method is applied to Benz- and$V$-type graphs, belonging to the genuine 3-loop topologies. In case of the$V$-type graphs with five massive propagators new types of nested sums anditerated integrals emerge. The sums are given in terms of finite binomially andinverse binomially weighted generalized cyclotomic sums, while the1-dimensionally iterated integrals are based on a set of $\sim 30$ square-rootvalued letters. We also derive the asymptotic representations of the nestedsums and present the solution for $N \in \mathbb{C}$. Integrals with apower-like divergence in $N$--space $\propto a^N, a \in \mathbb{R}, a > 1,$ forlarge values of $N$ emerge. They still possess a representation in $x$--space,which is given in terms of root-valued iterated integrals in the present case.The method of hyperlogarithms is also used to calculate higher moments forcrossed box graphs with different operator insertions.

Calculating Massive 3-loop Graphs for Operator Matrix Elements by the Method of Hyperlogarithms