Is it possible to find
$$I = \int_{-\infty}^{\infty}\int_{-\infty}^0 \frac{e^{i\xi}e^{\eta}}{(\alpha-\xi)^2+(\beta-\eta)^2}((\alpha-\xi)+i (\beta-\eta)) \ d\eta d \xi, $$
in closed form?
2026-03-28 14:20:22.1774707622
Closed form solution for Beurling transform: a 2d integral
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