Find Function with r^2 Near Zero & Approaching 0

[intervoxel]

I'm looking for a function which has a behavior r^2 near zero and approaching fast to zero when r tends to infinity. Thanks for any hints.

 

[DrewD]

Multiply two functions together where one behaves like $r^2$ near zero (how about $r^2$) and the other behaves like 1 near zero and decays to zero more quickly than $r^2$ increases. After you get the basic second function you can manipulated it to make the product of the two functions fit other constraints you have.

 

[AlephZero]

You want to pick the "second function" to make life easy for whatever you are doing. There are plenty of options, like
$$\frac{r^2}{1 + r^3}, \quad r^2 e^{-r}, \quad \text{etc.}$$