The key word linked to contour integration is “analyticity” or the absense thereof:
(A.1) |
exists for every point
inside
.
In most cases we are actually interested in
functions that are
not analytic; if this only happens at
isolated points (i.e., we don’t consider a ”line of
singularities”, usually called a ”cut” or
”branch-cut”) we can still expand the function in a
Laurent series
(A.2) |
How we obtain the coefficients from the function is closely linked to the problem of contour integration.