RG/Padé estimate of the three-loop contribution to the QCD static potential function

The three renormalization-group-accessible three-loop coefficients of powers of logarithms within the MS series momentum-space for the QCD static potential are calculated and compared to values obtained via asymptotic Padé-approximant methods. The leading and next-to-leading logarithmic coefficients are both found to be in exact agreement with their asymptotic Padé-predictions. The predicted value for the third RG-accessible coefficient is found to be within 7% relative |error| of its true value for nf⩽6, and is shown to be in exact agreement with its true value in the nf→∞ limit. Asymptotic Padé estimates are also obtained for the remaining (RG-inaccessible) three-loop coefficient. Comparison is also made with recent estimates of the three-loop contribution to the configuration-space static-potential function.