Title: Non-integer iterates of analytic functions


Abstract: For given function f, superfunction F is holomorphic 
solution of equation F(z+1)=f(F(z)). Superfunction F and its 
inverse G=F^{-1} allow to express the c-th iteration of f, as 
follows: f^{c}(z)=F(c+G(z)). In particular, 
h=Factorial^(1/2)=sqrt(!) is such function that h(h(z))=z!, and 
g=sqrt(exp) is such function that g(g(z))=exp(z). The complex 
maps and the algorithms for evaluation of such functions are 
presented.