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

Abstract

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 $xϵ[10^{-6},0.98]$.

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