# Contour integral with delta function

Using Cauchy's integral theorem how could we compute

$$\oint _{C}dz D^{r} \delta (z) z^{-m}$$

since delta (z) is not strictly an analytic function and we have a pole of order 'm' here C is a closed contour in complex plane

Can you find out for which z there is a pole?

If so, can you recall what Cauchy's integral theorem states?

matt grime
What does $$D^r$$ mean? Is it a constant, or a derivative operator?