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
$$\frac{r^2}{1 + r^3}, \quad r^2 e^{-r}, \quad \text{etc.}$$

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