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

The pure singlet asymptotic heavy flavor corrections to 3-loop order for the deep-inelastic scattering structure function F$_2$(x,Q$^2$)F$_2$(x,Q$^2$) and the corresponding transition matrix element View the MathML sourceAQq(3),PS in the variable flavor number scheme are computed. In Mellin-N space these inclusive quantities depend on generalized harmonic sums. We also recalculate the complete 3-loop pure singlet anomalous dimension for the first time. Numerical results for the Wilson coefficients, the operator matrix element and the contribution to the structure function F$_2$(x,Q$^2$)F$_2$(x,Q$^2$) are presented