= Quadratic stationary endpoint with quadratically vanishing amplitude
{title2=$\int_0^b e^{ixt^2}a(t)\,dt,\quad a(t)=ct^2+O(t^4)$}
The stationary endpoint contributes $ce^{3i\pi/4}\sqrt\pi/(4x^{3/2})$ by <method of steepest descent> along $t=e^{i\pi/4}r$. Its ordinary $x^{-1/2}$ term vanishes because $a(0)=0$. A nonstationary upper endpoint with $a(b)\neq0$ contributes $a(b)e^{ixb^2}/(2ibx)$ and therefore dominates the stationary contribution. The <stationary phase method> must retain both this boundary term and the first nonzero local-amplitude term.
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