\[

x^{-n}e^{-\frac{1}{2}\left(\frac{\delta}{x}\right)^{2n}}\approx\begin{cases}

x^{-n} & |x|>\delta\\

0 & |x|<\delta

\end{cases}

\]

For $\delta > 0$, $n\in\mathbb{N}_{1}$. I imagine this may help with unstable simulations of inverse square law type interaction.

Integral is really nice too (for n

__>__2), by diverging for small δ, means it could possibly used for renormalization work?

\[

\int_0^{\infty} dx\ x^{-n}e^{-\frac{1}{2}\left(\frac{\delta}{x}\right)^{2n}}\sim\delta^{-n+1}

\]

See WA for some plots.