Change of base formula for Tetration

[bo198214]

For a=3.0, b=1.5, the constant mu_b(a) is going to be something in the neighborhood of 10. So, yeah, if you try to set x=-10 or thereabouts, it's not going to converge properly.

Ok, this was a misreading of mine, I thought you sayed that \( \mu_b(a)<0 \) in this case.

Ok it seems to converge for \( a>b \) too, though there is no proof.

So what about the case \( b<\eta \) then? I mean this is what we want: \( b\le\eta \) and \( a>\eta \).