Asymptotic developments of the solutions of the translation equation (Q686404)

For a real solution of \(F(x,s+t)=F \bigl( F(x,s),t \bigr)\) and \(F(x,0)=x\) it is assumed that, in a neighborhood of 0, both partial derivatives exist and there exists a termwise differentiable asymptotic expansion \(\sum f_ n(xt)x^ n\). The author offers differential recursion formulas for \(f_ n\).