Suppose I have a function
$n(r)=\text{A}_i(ar)\int_1^r\xi_1{e^{-b\xi_1^2}}\text{B}_i(a\xi_1)d\xi_1-\text{B}_i(ar)\int_1^r\xi_2{e^{-b\xi_2^2}}\text{A}_i(a\xi_1)d\xi_1$
where $\text{A}_i$ and $\text{B}_i$ are the Airy Functions.
Note that for large $r$ $\text{A}_i$ decays to zero, whereas $\text{B}_i$ explodes to infinity. Because we have $\sim$ the product of these two functions, it means that the limit for large $r$ is controlled.
The constants are of the order $a\sim10^{10}$ and $b\sim10^3$ and $r\in[0,1]$.
Now, the problem is that I want to make a plot of $n(r)$, but to do so I have to perform a numerical integration. You can start to see that this raises problems because the computer won't be able to calculate $\text{A}_i$ nor $\text{B}_i$ at the desired argument due to the large value of $a$- although we know that analytically the desired final result, after the product with the $\text{A}_i$ or $\text{B}_i$ terms, respectivelly (I think that the term $\xi e^{-b\xi^2}$ is not relevant for the discussion), would be a nice "controllable" value.
NOTE: the dimension of the variable $a$ is meter$^{-1}$ and of $r$ is meter, which means that even with a change of units, the argument of the Airy functions will still be the same (it's an adimensional argumental, as it should be).