I have been grouping functions based on how their graph looks like. I started with bell-shaped curves and have come up with the following functions:
- cos, sin
- sech (from -1 to 1)
- Infinitely Smooth Radial Basis Functions (RBFs)
- Bump functions (to a certain extent)
- Polynomials (few cases)
What more I can add to this list? I am unable to come up with something new.
Note: The functions should be simple and do not involve piecewise definitions (like Irwin-Hall distribution) or repetitive operations (summations/series/integrals etc.).