"circular" operators, "circular" derivatives, and "circular" tetration.

[Catullus]

Now that was all fairly simple to understand, but now we come to the part where we must define circular multiplication.  It's still fairly simple, but may seem a bit awkward.

\( x \odot (x^{\circ n}) = x^{\circ n+1} \)

cxp(3π/4)=0. If , then  would equal cxp(3π/4+1)=-√(2)sin(1)~-1.190.
cxp(-π/4)=0. If , then  would equal cxp(-π/4+1)=sin(1)~0.841.