# Special function

1. Mar 24, 2014

### 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.

2. Mar 24, 2014

### 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.

3. Mar 24, 2014

### AlephZero

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