Iteration basics

[Gottfried]

So I have a question now:

Is it possible to integrate /differentiate iterated functions over iteration parameter (e.g. t in fot(x)) if that is continuous real or complex number in some interval?

Ivars

According to my derivations in Continuous Iteration we have if base b=e^(1/e) a powerseries in h (if h is the height parameter) which may then be differentiated/integrated by usual diff/int of terms. If base b differs from this, we have, due to eigensystem-analysis a series, where h is in the exponent, thus a modified dirichlet-series (I'd say). This can also be diff'ed/int'ed termwise, but has then something like a*u^h and the derivative of such a term is then a*log(u)*u^h
Gottfried