Theory: Where does 1/h come from in Kernel Constant?


I always struggle a bit with theory, so please bare with me.

On pySPH I found the following equation for the Gaussian kernel:

And I can prove that the normalization constant in 1D should be 1/sqrt(pi). But I noticed that for every step up in dimension, we would add another "*1/h". Where does this come from?

Is it simply a way to give our kernels units of inverse position, i.e. 1/m for 1D etc. Just want to understand better.

Kind regards

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