= Quadrant modified Helmholtz Dirichlet Poisson formula
{title2=$q(x,y)=\frac2\pi\int_0^\infty[\sin(px)e^{-B(p)y}S_2(p)+\sin(py)e^{-B(p)x}S_1(p)]dp$}
Here $B(p)=\sqrt{p^2+4\lambda}$ and $S_j$ are the <Fourier sine transforms> of the boundary values. The <modified Helmholtz closed spectral one-form> and its reflected <global relations> remove the unknown normal traces. Equivalently, four reflected <fundamental solutions> give a zero-boundary <Green function> in the quadrant. Its inward derivatives give the displayed formula. The two terms recover the bottom and left traces respectively; matching corner values ensure continuity at the corner.
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