Evaluation ofηin Wilson's Incomplete-Integration Method: Independence of Cutoff Parameters to Orderε2

The expression for the coefficient of ${\epsilon }^2$ in the $\epsilon$ expansion for the critical exponent $\eta$ of the Ising model has been obtained by Shukla and Green within the incomplete-integration method of Wilson. It was left by them in the form of an unevaluated integral, which appears to depend on parameters characterizing details of the renormalization-group procedure. The integral is evaluated here and found to equal $\frac{1}{54}$, regardless of the values of those parameters.