Fractional iteration of x^2+1 at infinity and fractional iteration of exp

[JmsNxn]

To be honest, this sounds like a very tangible approach to solving for the half-iterate of \( exp \), one that I can actually understand straight-up (even though I have a poor understanding of how Schroder's method works, I still understand that it works ).

I wonder if this method agrees with any other methods of extending tetration? Have you been able to compute anything yet involving exp, or is it all still theoretical?

I'm very interested in seeing how this evolves.