Hyperbolic tangent. The slightly uglier younger brother of the tan function.
Basically a smooth sigmoidal function that pops up in a lot of places in physics
It happens to be a pretty good approximation to the saturation behavior of an operational amplifier. Those things are everywhere in electronics.
It's pretty expensive though, so I use cheaper approximations where I can do so without sacrificing sound.
Since tan was mentioned, the hyperbolic trig functions are to x^2-y^2=1 what the regular trig functions are to x^2+y^2=1. Rather than describing things to do with circles, they describe things to do with hyperbola. They come up quite a bit considering they're the solution of some differential equations.