Hi Folks,
I am working through a theorem involving the delta function. I have some queries in the early stages of derivation. See attached.
Thanks
1. There is k -th derivative of delta function and differencial of k-th derivative
gives k+1 derivative.
2. The k-th derivative of delta function at $\displaystyle \pm \; \infty$ =0.
You may think delta function being proportional to $\displaystyle e^{-x^2}$.
Yes, they are treated differently.
Please look here
Delta Function -- from Wolfram MathWorld
(17) equation.
For k-th derivative we write
$\displaystyle
\delta^{(k)}
$
and k-th degree
$\displaystyle
x^{k}.
$