= Formal pseudodifferential wave function
{title2=$w=k^\beta e^{kx}\sum_{i\geq0}w_i(x)k^{-i}$}
Treat $k$ as a formal spectral parameter near infinity. If $P=\sum_{j\geq0}g_j\partial^{\alpha-j}$, the <formal pseudodifferential composition rule> gives $Pw=k^{\alpha+\beta}e^{kx}\sum_{s\geq0}k^{-s}\sum_{i+j+r=s}g_j\binom{\alpha-j}{r}w_i^{(r)}$. Each <coefficient> contains finitely many terms. This describes a formal module action, not a claim that the infinite series converges at finite $k$.
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