# Use Convolve with a Dirac Delta function?

**URL:** <https://community.wolfram.com/t/use-convolve-with-a-dirac-delta-function/13144>\
**Category:** Questions\
**Tags:** symbolic-computations\
**Created:** [October 3, 2018, 8:37am UTC](https://community.wolfram.com/t/use-convolve-with-a-dirac-delta-function/13144 "2018-10-03T08:37:08Z")\
**Posts on this page:** 3\
**Page:** 1

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**Author:** ![zpal](https://avatars.discourse-cdn.com/v4/letter/z/e9bcb4/32.png) [@zpal](https://community.wolfram.com/u/zpal)\
**Post date:** [October 3, 2018, 8:37am UTC](https://community.wolfram.com/t/use-convolve-with-a-dirac-delta-function/13144/1 "2018-10-03T08:37:08Z")

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In Wolfram Mathematica 11.3 Convolve[1, x_DiracDelta[x], x, y] gives no result. But the equivalent function Integrate[x_DiracDelta[x], {x, -[Infinity], [Infinity]}] gives the correct result which is 0.

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<div class="post-metadata">

**Author:** ![timmy2x](https://yyz1.discourse-cdn.com/wolfram/user_avatar/community.wolfram.com/timmy2x/32/14365_2.png) [@timmy2x](https://community.wolfram.com/u/timmy2x)\
**Post date:** [October 3, 2018, 1:50pm UTC](https://community.wolfram.com/t/use-convolve-with-a-dirac-delta-function/13144/2 "2018-10-03T13:50:35Z")

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Try setting the GenerateConditions option to True to find a conditional expression where the results are valid.

```
Convolve[x DiracDelta[x], g[x] , x, y, 
 GenerateConditions -> True] (* 0 *)
Convolve[g[x], x DiracDelta[x], x, y, 
 GenerateConditions -> True] (* 0 *)

```

It appears that the answer is “0” for all conditions and for any function, g[x].

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<div class="post-metadata">

**Author:** ![zpal](https://avatars.discourse-cdn.com/v4/letter/z/e9bcb4/32.png) [@zpal](https://community.wolfram.com/u/zpal)\
**Post date:** [October 3, 2018, 1:58pm UTC](https://community.wolfram.com/t/use-convolve-with-a-dirac-delta-function/13144/3 "2018-10-03T13:58:33Z")

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Yes, with this option it works properly.