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Infinite tetration and superroot of infinitesimal
#86
Ivars Wrote:
bo198214 Wrote:
Ivars Wrote:Barrows said:
"... if x^x=1/2 has no solutions in real and complex numbers ... "
But ... :



He actually wrote he does not know if it has. "There is no square superroot of 1/2, " . And it was Bromer in 1987 article. So it has solution in complex numbers.

x= e^W(W(-ln2/2)).
Actually, the beautiful formula I propose is:
ssqrt(x) = ln(x) / W(ln(x)), which, for x = 1/2, gives:

ssqrt(1/2) = ln(1/2) / W(ln(1/2)) = 0.26289282802173525.. + 0.4996694356833174.. i

Perfectly coherent with Henryk's formula.

GFR
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