= Cubic exponential integral Stokes sectors
{title2=$G(z)=\int_0^1e^{-z^3t^3}dt$}
The saddle and endpoint <asymptotic expansions> of this <entire function> have algebraic coefficients $C\omega^j/z$ in sectors $(2j-1)\pi/3<\arg z<(2j+1)\pi/3$, where $C=\Gamma(1/3)/3$ and $\omega=e^{2\pi i/3}$. Deforming the contour onto the decay ray $\arg(zt)=2j\pi/3$ gives its complete integral $C\omega^j$. The endpoint contribution is $-e^{-z^3}(3z^3)^{-1}\sum_{r\geq0}(-1)^r(2/3)_r/z^{3r}$. The algebraic coefficient switches at $\arg z=\pi/3,\pi,5\pi/3$; the equal-exponential-magnitude <anti-Stokes lines> are the intervening rays $\pi/6+j\pi/3$.
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