Prove Idntity - Dirac Delta - Distributions

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Drazick
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Homework Statement


The Identity to prove:
Identity: x^m times the n-th derivative of the Dirac delta at x equals (-1)^m times n! over (n-m)! times the (n-m)-th derivative of the Dirac delta at x, for m less than or equal to n.


Homework Equations


Using Integration by parts



The Attempt at a Solution


I couldn't produce the denominator.
 

Discussion

Hi Drazic, welcome to PF!:smile:

Drazick said:

Homework Statement


The Identity to prove:
Equation: x^m δ^(n)(x) = (-1)^m n!/(n-m)! δ^(n-m)(x), for m ≤ n, with δ^(n) denoting the nth derivative of the Dirac delta.


Homework Equations


Using Integration by parts



The Attempt at a Solution


I couldn't produce the denominator.

Post your calculations, and we'll be able to help.
 

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