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This work was carried out in 1985. It was published in Russian in Yad. Fiz.44, 498 (1986) [English translation Sov. J. Nucl. Phys. 44, 321 (1986)]. Noneof these publications are available on-line. Submitting this paper to ArXivwill make it accessible. *** A simple method is developed that makes itpossible to determine the $k$-loop coefficient of the $\beta$-function if theoperator product expansion for certain polarization operators in the $(k -1)$loop is known. The calculation of the two-loop coefficient of the Gell-Mann-Lowfunction becomes trivial -- it reduces to a few algebraic operations on alreadyknown expressions. As examples, spinor, scalar, and supersymmetricelectrodynamics are considered. Although the respective results for$\beta^{(2)}$ are known in the literature, both the method of calculation andcertain points pertaining to the construction of the operator product expansionare new.

Operator Product Expansion and Calculation of the Two-Loop Gell-Mann-Low Function