What is the definition of D^m delta(e^D) in this formula?

[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 $$D^{m} \delta (e^{D})$$

 

[mathman]

Something is wrong with your latex expressions. They are unreadable.

 

[Feldoh]

This thread might help w/ the latex: https://www.physicsforums.com/showthread.php?t=8997