z^^z ?

[Stan]

About the complex tetration thing...

I thought (intuitively) that:

e^^xi=cos(x)+sin(x)i

e^^2xi=cos(cos(x)+sin(x)i) + sin(cos(x)+sin(x)i))

e^^3xi=cos(cos(cos(x)+sin(x)i) + sin(cos(x)+sin(x)i)))
sin(cos(cos(x)+sin(x)i) + sin(cos(x)+sin(x)i)))

e^^kxi=cos(cos(cos(cos(x)+sin(x)i) + sin(cos(x)+sin(x)i)))
sin(cos(cos(x)+sin(x)i) + sin(cos(x)+sin(x)i)))) +....2^k times
sin(cos(cos(cos(x)+sin(x)i) + sin(cos(x)+sin(x)i)))
sin(cos(cos(x)+sin(x)i) + sin(cos(x)+sin(x)i))))...etc....

But this is MERELY an intuitive hunch.

Any thoughts on the matter?