Also look at the differences of that values; this is even more suggestive because of the typical pattern which suggests, that the differences of the logs grow asymptotic linearly with the logs of the index, which is just another expression for hypergeometric growthrate. So the convergence-radius for the half-iterate seems to be zero as is for the half-iterate of $exp(x)-1$ .
Also look at the differences of that values; this is even more suggestive because of the typical pattern which suggests, that the differences of the logs grow asymptotic linearly with the logs of the index, which is just another expression for hypergeometric growthrate. So the convergence-radius for the half-iterate seems to be zero as is for the half-iterate of $exp(x)-1$ .