Comparing the Known Tetration Solutions

[bo198214]

As you can see, when the base is between \( 1<b<\eta \), although the matrix equation has a solution, the solutions (coefficients) do not seem to converge. This is what leads me to beleive that my super-logarithm definition will only work for \( b>\eta \).

For me they look pretty convergent, they are divergent at 1. But for \( b>1 \) they always become "dense in line" which represents the limit. The only thing is that the more b approaches 1 the longer it takes until it stabilizes, so for some small b it hasnt stabilized for n<10 but the tendency to built a dense line is recognizable, I think.