# Residue of Dirac delta function?

1. Oct 18, 2013

Does the Dirac delta have a residue? It seems like it might, but I don't know how to attack it, since I really know very little about distributions. For example, the Dirac delta does not have a Laurent-expansion, so how would you define its residue?

2. Oct 18, 2013

### stephenkeiths

Perhaps you could try using something that approaches a delta function like $\frac{1}{\pi} \frac{sin(\lambda x)}{x}$ as $\lambda \to \infty$ or maybe $\sqrt{\frac{\alpha}{\pi}}e^{-\alpha x^2}$ as $\alpha \to \infty$

Perhaps you could find the residue w.r.t. $\lambda$ and take the limit. Not sure, just something to maybe try.

3. Oct 18, 2013

### h6ss

Have you tried extending the Dirac delta to the complex plane and then examining its poles?

4. Oct 22, 2013