OFFSET
1,1
LINKS
Jonathan Sondow, Diego Marques, Algebraic and transcendental solutions of some exponential equations, Annales Mathematicae et Informaticae 37 (2010) 151-164.
FORMULA
x0 = -((x*ProductLog(-1, -(log(x)/x)))/log(x)), with x = 5/2, where ProductLog is the Lambert W function.
EXAMPLE
x0 = 2.97028705025575877937998429103168637323950439632715025453459...
z = x0^(5/2) = 15.20533715980107653442006557792026842686895921352582...
z > e^e = 15.15426224... = A073226.
MATHEMATICA
x0 = -((x*ProductLog[-1, -(Log[x]/x)])/Log[x]) /. x -> 5/2; RealDigits[x0, 10, 102] // First
CROSSREFS
KEYWORD
AUTHOR
Jean-François Alcover, Jun 01 2015
STATUS
approved