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tetration solution f(b)
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let x >= e

consider b^x

take the regular half-iterate of b^x at the largest fixpoint, for b in ]sqrt(2),eta[ for a fixed value of x ( again >= e : say 3 ) , and express that as a taylor series of b.

call that f(b) and now consider f(e).

f(e) = half - iterate exp at value 3.

regards

tommy1729

( more later )