easing functions that accept influence and speed as argument

I've found some functions that can be used in expressions to control easing: jquery-easing/jquery.easing.js at master · danro/jquery-easing · GitHub . You can see how each one looks here: Easing Functions Cheat Sheet

This functions are discrete, meaning each function produces one curvature of the animation. If you played with graph editor, you can see that AE easing gives you handles, that produce continuous curvatures of the animation. You can also type in any influence and speed you want.

So my question is, where can I find easing functions that AE uses that accept influence and speed for an argument? With the functions I posted, you are limited to a small subsection of possibilities. Can this function be derived from the ones I posted? If so, whats the relation between them?