Interesting value for W, h involving phi,Omega?

[Ivars]

Since

z=W(z)*e^W(z)

ln(z)=lnW(z)+W(z)

ln(W(z))=ln(z)-W(z)

h(W(z)^(1/(W(z))=W(z)

and

ln(W(z)^(1/W(z))= (1/W(z))*ln(W(z)= ln(z)-W(z)/W(z)=ln(z)/lnW(z)-1

In base W(z) that would be just log base W(z) (z)-1

ln (W(z)^(1/W(z))= W(z)/ln(W(z))= ln(z)/lnW(z)-1 = log base W(z) (z)-1

then

h(W(z)^(1/W(z))= -W(-(log base W(z) (z))+1) /((log base W(z) (z))-1))

So now there is a continuous (?) base for logarithms that gives infinite tetration result, if tetrated number is representable as self root of W function.

Superroot: Ssroot(W(z)^(1/W(z)) = ((log base W(z) (z))-1)) /W((log base W(z) (z))-1)