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.