Theorem on increment of tetration
Let \(F\) be solution of equation
for some \(\beta>0\).
Let \(L\) be the fixed point, id est, \(\exp(\beta L)=L\)
Let \(F(z)=L+\varepsilon+O(\varepsilon^2) \)
where \(\varepsilon = \exp(kz) \) for some increment \(k\).
Let \(~ K\!=\!\exp(k)\)
\( \Im(K) = \Im(k) \)