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The pure singlet asymptotic heavy flavor corrections to 3-loop order for thedeep-inelastic scattering structure function $F_2(x,Q^2)$ and the correspondingtransition matrix element $A_{Qq}^{(3), \sf PS}$ in the variable flavor numberscheme are computed. In Mellin-$N$ space these inclusive quantities depend ongeneralized harmonic sums. We also recalculate the complete 3-loop pure singletanomalous dimension for the first time. Numerical results for the Wilsoncoefficients, the operator matrix element and the contribution to the structurefunction $F_2(x,Q^2)$ are presented.

The 3-Loop Pure Singlet Heavy Flavor Contributions to the Structure Function $F_2(x,Q^2)$ and the Anomalous Dimension