= Polygonal modified Helmholtz global relation
{title2=$\sum_j\int_{-1}^1W_j(s,\lambda)ds=0$}
For $u_{z\bar z}=\beta^2u$, pull back its spectral <closed differential one-form> along each straight side $z=m_j+sh_j$. Under counterclockwise traversal and outward <normal derivatives> $q_j$, the side density is $i e^{-i\beta(\lambda z-\bar z/\lambda)}[|h_j|q_j+\beta(\lambda h_j+\bar h_j/\lambda)g_j]$, where $g_j$ is the <Dirichlet boundary data>. The <Generalized Stokes theorem> gives the displayed <global relation>. Clockwise traversal reverses the normal-derivative coefficient; all orientations must be changed consistently.
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