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<math display="block">\epsilon^2\left[\frac{1}{\delta^2} \left(\sum_{n=0}^\infty \delta^nS_n'\right)^2 + \frac{1}{\delta} \sum_{n=0}^{\infty}\delta^n S_n''\right] = Q(x).</math>
To [[leading-order|leading order]] in ''ϵ'' (assuming, for the moment, the series will be asymptotically consistent), the above can be approximated as
<math display="block">\frac{\epsilon^2}{\delta^2} S_0'^2 + \frac{2\epsilon^2}{\delta} S_0' S_1' + \frac{\epsilon^2}{\delta} S_0'' = Q(x).</math>
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