Sometimes, you need to compute a function that’s complex, cumbersome, or which your favorite language doesn’t quite provide for. We may be interested in an exact implementation, or in a sufficiently good approximation. For the later, I often turn to Abramovitz and Stegun’s *Handbook of Mathematical Function*, a treasure trove of tables and approximations to hard functions. But *how* do they get all these approximations? The rational function approximations seemed the most mysterious of them all. Indeed, how can one come up with

for , for ?

Well, turns out, it’s hard work, but there’s a twist to it. Let’s see how it’s done!