It is assumed that a sum rule of the Bloom and Gilman type applies to the photon structure function $\nu W_2^{\gamma }(q^2,\nu )$ and the scaling limit function $\nu W_2^{\gamma }\left(\omega \right)$, where $\omega =-\frac{2\nu }{q^2}$. We consider a dominating resonance for photon-photon scattering and find from the sum rule that the form factor depends only on $q^2$.

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