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The anomalous magnetic moment of the muon is one of the most fundamentalobservables. It has been measured experimentally with a very high precision andon theory side the contributions from perturbative QED have been calculated upto five-loop level by numerical methods. Contributions to the muon anomalousmagnetic moment from certain diagram classes are also accessible by alternativemethods. In this paper we present the evaluation of contributions to the QEDcorrections due to insertions of the vacuum polarization function at five-looplevel.

The QED vacuum polarization function at four loops and the anomalous magnetic moment at five loops