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We verify the identity which relates the two-point Green functions of ${\calN}=1$ SQED with $N_f$ flavors, regularized by higher derivatives, by explicitcalculations in the three-loop approximation. This identity explains why in thelimit of the vanishing external momentum the two-point Green function of thegauge superfield is given by integrals of double total derivatives in themomentum space. It also allows to derive the NSVZ $\beta$-function exactly inall loops if the renormalization group functions are defined in terms of thebare coupling constant. In order to verify the considered identity we use itfor constructing integrals giving the three-loop $\beta$-function starting fromthe two-point Green functions of the matter superfields in the two-loopapproximation. Then we demonstrate that the results for these integralscoincide with the sums of the corresponding three-loop supergraphs.

Relation between two-point Green functions of ${\cal N}=1$ SQED with  $N_f$ flavors, regularized by higher derivatives, in the three-loop  approximation