= Polynomial source function moments for emergent intensity
{title2=$A_j=j!a_j$}
= Emergent-intensity polynomial coefficients
{synonym}
For a semi-infinite plane-parallel atmosphere with polynomial <source function> $S(\tau)=\sum a_j\tau^j$, the outward <specific intensity> is $\int_0^\infty S(\tau)e^{-\tau/\mu}\,d\tau/\mu$. Substitution $u=\tau/\mu$ gives coefficients $A_j=j!a_j$ in the surface polynomial in $\mu$. The deep boundary term must vanish. A local truncated Taylor series instead gives this contribution plus a remainder, so its surface polynomial is not automatically exact.
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