Computing DIS coefficient functions at 4-loop

I'll will discuss our recent progress in computing the non-singlet nf^2 contribution to the DIS coefficient functions at 4-loop. The computation is performed in Mellin space by employing a system of differential equations to generate a finite expansion in Mellin moments. The computation of the Mellin moments via this technique allows us to extract a number of moments large enough to reconstruct the all-order expression in terms of harmonic sums and map it back to x-space. To conclude I'll discuss further applications of this method and how we plan to adapt it for more complicated computations.