I'm learning about the WKB method, and I'm applying it to an assignment.
The assignment question asks to find the "leading order" WKB expansion for the particular equation.
For WKB you make the substitution: $$y \sim \exp \left[\frac{1}{\delta}\sum_{n=0}^{\infty} \delta ^n S_n(x)\right], \delta \to 0$$ I'm fine with this, I can manipulate it, solve for $S_n(x)$ etc.but I'm unsure as to what "leading order" means in this context.
For other asymptotic methods when you have $y=y_0+\epsilon y_1+\dots$, it's obvious, you just take the terms multiplying $\epsilon^0$, but it doesn't happen the same in WKB because the $\epsilon$s are in the exponential.
So, what does "leading order" mean for WKB?