Winding direction: With residues, is there some trick to picking the winding direction or do I just get to pick what I want? I'm specifically looking at the solution to the Klein-Gordon equation. It appears that all the sources are just picking the winding direction that is handy. For this specific problem, that's fine because it has a multitude of eigenvalues.
However, in general, is there any trick to picking a winding direction OR do contour integrals always have multiple answers?