can someone offer a clear conceptual treatment of contour consideration in residue theorem? How can I judge which residues to accept and which to reject when the limits of the integral is from -infinity to +infinity?
For example, an integration is:
d21 = (-kp v + delta_p + i gamma_21)
d31 = (-kp v - kc v + (delta_p + delta_c) + i gamma_31)
and the function in the integral is: f(v)=vT/((v^2+vT^2)pi^1/2)
Could anybody help out solving this integral for v.
The following statement isn't quite precise enough for universal application, but can be useful: Singularities to the left of a person following the path of integration are included, singularities to the right are excluded. For a person walking along the real axis from $-\infty$ to $\infty$, there is no ambiguity: the singularities in the upper half plane are on the left and the singularities in the lower half plane are on the right. Se we keep the singularities in the upper half plane. (If the singularity lies on the path, there are a variety of ways to proceed -- more detail would be needed.)