Derivatives of the Dirac Delta

I’ve been thinking lately about derivatives of the Dirac delta function. In particular, how to obtain formulas like

and similar, more complicated expressions for higher derivatives. In the above formula, the function is assumed to have a single zero at , and all of the derivatives on the right-hand side are evaluated at . If would have multiple zeroes, the right-hand side would include a sum over all the zeroes.

Deriving these formulas isn’t that hard, but I’ve been trying to come up with some nice applications; perhaps they might be useful in the electrodynamics of infinite curves, rather than straight lines of charge. You can also use them to evaluate integrals such as

Welcome!

Hi everyone!

This is my new website. I am currently working on transferring things over from my old site on Wordpress. Be sure to check back over time as I accumulate more material here.