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

  title={Analytic Continuation of the Harmonic Sums for the 3-Loop Anomalous Dimensions},
  author={J. Blumlein and S. Moch},
  journal={Physics Letters B},
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 x ∈ [ 10 −6 , 0.98 ] . 

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