Did we mention already the tangent? It has this nice addition theorem:

which brings us the superfunction:

for the function

is another particular case of a linear fraction (where the regular iteration at both fixed points coincide).

The two (non-real) fixed points are:

,

for

which brings us the superfunction:

for the function

is another particular case of a linear fraction (where the regular iteration at both fixed points coincide).

The two (non-real) fixed points are:

,

for