Strange formula

1. Aug 16, 2008

mhill

let be the identity

$$(2 \pi ) i^{m-1}D^{m} \delta (u) = \int_{-\infty}^{\infty} dx e^{iux}x^{m-1}$$`

then making the replacement u=e^D D derivative with respect to 'x' then

$$(2 \pi ) i^{m-1}D^{m} \delta (e^{D})f(0) = \int_{-\infty}^{\infty} dx e^{ixe^{D}}x^{m-1}f(0)=\int_{-\infty}^{\infty} dx x^{m-1}\sum_{k=0}^{\infty}\frac{i^{k}f(n)}{n!}$$

the problem is that i do not know how to define $$D^{m} \delta (e^{D})$$

Last edited by a moderator: Aug 19, 2008
2. Aug 17, 2008