The O(αs3) massive operator matrix elements of O(nf) for the structure function F2(x,Q2) and transversity

The contributions ∝nf to the O(αs3) massive operator matrix elements describing the heavy flavor Wilson coefficients in the limit Q2≫m2 are computed for the structure function F2(x,Q2) and transversity for general values of the Mellin variable N. Here, for two matrix elements, Aqq,QPS(N) and Aqg,Q(N), the complete result is obtained. A first independent computation of the contributions to the 3-loop anomalous dimensions γqg(N), γqqPS(N), and γqqNS,(TR)(N) is given. In the computation advanced summation technologies for nested sums over products of hypergeometric terms with harmonic sums have been used. For intermediary results generalized harmonic sums occur, while the final results can be expressed by nested harmonic sums only.