A troubling question that occured to me is if my derivation of the Taylor's series of \( f^n(z) \) is correct, due to its generality it must contain all solutions that don't have a super-attracting fixed point. Since all functions except the successor function have finite fixed points, if f(z) is smooth then my approach should be valid. So shouldn't all valid methods give the same results? Yeah, lots of different tetrations and all, but shouldn't they all agree on their common areas? Aren't we all studying parts of the same "elephant"?
Daniel