= Negative-index scalar Riemann-Hilbert moment conditions
{title2=$\int_Lt^j g(t)\,dt=0\quad(0\le j<q)$}
Suppose a scalar canonical factor has exterior growth $X_-(z)\sim z^q$ with index $-q<0$, and the original exterior unknown must decay as $O(z^{-1})$. Dividing by the canonical factor gives an additive jump $D_+-D_-=g$ with exterior decay $O(z^{-q-1})$. The exterior <Cauchy integral> expands in moments $-\int_Lt^jg(t)dt/(2\pi iz^{j+1})$. Its first $q$ coefficients must therefore vanish, yielding the displayed solvability conditions. Under this decay there is no nonzero entire <polynomial> addition. A nonlocal moment appearing in $g$ must additionally agree with the moment of the reconstructed original jump.
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