Deriving tetration from selfroot?

[Ivars]

As far as I understand selfroot and any root:

Selfroot is x^(1/x):

Selfroot =

For positive x, is real, giving one real self root (k=0) , and infinite number of imaginary roots depending on ratio .

For negative x, will be imaginary, of the form:

so roots are:

, again infinite quantity in totality. m=0 gives:

,


For imaginary and complex x, tomorrow, with mistakes here also hopefully corrected.

Ivars

[Ivars]

Selfroot is x^(1/x):

Selfroot =

For Imaginary x, will be imaginary, of the form:

so roots are:

, again infinite quantity in totality. n=0 gives:

,

If

,

,

For n=0, k=0

,

Something wrong again; I will correct later.

Ivars