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Gorishny, Kataev, Larin, and Surguladze have calculated the four-loop corrections to the QED Gell-Mann-Low function psi and also to the on-shell Callan-Symanzik Beta function, which then enables a determination of the vacuum-polarization coefficient a3. We have verified their results by explicitly checking that psi satisfies the Gell-Mann-Low equation to order (alpha/pi) 4. The (alpha/pi) 4 -order term requires the asymptotic photon propagator to order (alpha/pi)5, and the vanishing of (alpha/pi) 4 -order terms enables a determination of the fifth-order vacuum-polarization coefficient b 4 = 12.8648.
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