OFFSET
2,1
COMMENTS
It has not yet been determined if this number has a closed form.
FORMULA
The derivative x^y = y, or y = -ProductLog(-Log(x))/Log(x) when solved for y, is the function in which this value is a root. The derivative is (ProductLog(-Log(x))^2)/((x*Log(x)^2)*(1+ProductLog(-Log(x))).
EXAMPLE
78.5176688733806851928297599903919937600495951319589367155801108473527173126...
MATHEMATICA
FindRoot[Re[ProductLog[-Log[x]]^2/(x Log[x]^2 (1 + ProductLog[-Log[x]]))], {x, 78, 79},
WorkingPrecision -> 261]
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
David D. Acker, Sep 26 2016
STATUS
approved