- #1

rms502

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I just wondered whether there was any standard identity to help me solve this equation:

$$ \int \delta(f(x))^{\prime\prime}g(x) dx $$

Thanks in advance for your help.

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- Thread starter rms502
- Start date

- #1

rms502

- 1

- 0

I just wondered whether there was any standard identity to help me solve this equation:

$$ \int \delta(f(x))^{\prime\prime}g(x) dx $$

Thanks in advance for your help.

- #2

mathman

Science Advisor

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I am not sure what you mean by the derivative of the delta function (derivative with respect to what?).

Integration by parts twice might be an approach.

- #3

lurflurf

Homework Helper

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$$

\delta(\mathop{f}(x))''=\mathop{f}''(x) \delta (x)+(\mathop{f}'(x))^2 \delta '' (x) \\

\int \! \delta ^{(n)} (x) \, \mathop{f} (x) \, \mathop{dx}=(-1)^n\int \! \delta (x) \, \mathop{f ^{(n)}} (x) \, \mathop{dx}\\

\int \! \delta (\mathop{f} (x)) \, \, \mathop{g} (x) \mathop{dx}=\sum_{x \in f^{-1}(0)} \mathop{g}(x)

$$

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