Well, the use of the Lambert Function, for finding back x in y = x^x, is an old affair. The point is that, the present Wikipedia formula seems to covers only the "upper branch" of ssqrt(x), if we only use the W(0) "classical" branch, as it seems to be indicated, afaik (as far as I know), in the the first wikiplot of the W article..
A more complete ssqrt formula should also cover its "lower branch". The definition of "plog(x)" as the logical union of the two W(0) and W(-1) product logarithm real branches will do the business. But, I am sure that Henryk will amend and upgrade the tetration article, accordingly.
GFR
A more complete ssqrt formula should also cover its "lower branch". The definition of "plog(x)" as the logical union of the two W(0) and W(-1) product logarithm real branches will do the business. But, I am sure that Henryk will amend and upgrade the tetration article, accordingly.
GFR