Analytic Continuation of the Harmonic Sums for the 3--Loop Anomalous Dimensions

We present for numerical use the analytic continuations to complex arguments of those basic Mellin transforms, which build the harmonic sums contributing to the 3–loop anomalous dimensions. Eight new basic functions contribute in addition to the analytic continuations for the 2–loop massless Wilson coefficients calculated previously. The representations derived have a relative accuracy of better than ${10}^{-7}$ in the range $xϵ[{10}^{-6},0.98]$.