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

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- Dec 5th 2010, 10:53 AMbugatti79Theorem involving delta function: proof by induction
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 - Dec 8th 2010, 03:04 PMzzzoak
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 $\displaystyle e^{-x^2}$. - Dec 9th 2010, 10:58 AMbugatti79
- Dec 9th 2010, 01:14 PMzzzoak
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}.

$ - Dec 12th 2010, 02:30 AMbugatti79
- Dec 12th 2010, 10:37 AMzzzoak
I am not sure you have some problems with this line

$\displaystyle

(-1)(-1)^k \; (k+1)k! \; = \; (-1)^{k+1} \; (k+1)! \; \; ?

$ - Dec 12th 2010, 10:41 AMbugatti79
- Dec 16th 2010, 10:51 AMbugatti79
(k+1)!=(k+1)k! and (-1)(-1)^k=(-1)^(k+1)

Cheers