New posts in Fractional Iteration

half iterate of $x^2+c$

Is there an "elegant" non-recursive formula for these coefficients? Also, how can one get proofs of these patterns?

"Closed-form" functions with half-exponential growth

Do maps have flows?

What's a natural candidate for an analytic function that interpolates the tower function?

solving $f(f(x))=g(x)$

f(f(x))=exp(x)-1 and other functions "just in the middle" between linear and exponential