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The contributions $\propto n_f$ to the $O(\alpha_s^3)$ massive operatormatrix elements describing the heavy flavor Wilson coefficients in the limit$Q^2 \gg m^2$ are computed for the structure function $F_2(x,Q^2)$ andtransversity for general values of the Mellin variable $N$. Here, for twomatrix elements, $A_{qq,Q}^{\sf PS}(N)$ and $A_{qg,Q}(N)$, the complete resultis obtained. A first independent computation of the contributions to the3--loop anomalous dimensions $\gamma_{qg}(N)$, $\gamma_{qq}^{\sf PS}(N$ and$\gamma_{qq}^{\sf NS,(TR)}(N)$ is given. In the computation advanced summationtechnologies for nested sums over products of hypergeometric terms withharmonic sums have been used. For intermediary results generalized harmonicsums occur, while the final results can be expressed by nested harmonic sumsonly.

The O(\alpha_s^3) Massive Operator Matrix Elements of O(n_f) for the Structure Function F_2(x,Q^2) and Transversity