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Superroots and a generalization for the Lambert-W
#17
@andrew

Congrats with your result.

@gottfried

The thing is solving (x_m ^ x_m)^[m] = y is only close to solving
X_n^^[n] = y ( n = m in value )
When

Y is large and n (or m) is small.

For instance x in x^x^x^x = 2000 is close to

Y in (y^y)^(y^y) = 2000.

But a in a^a^a^a = 2,718 is different from
B in (b^b)^(b^b) = 2,718.

This is logical considering the fixpoint

X^x = x

Gives x = {-1,1}.

So one method is attracted to eta and the other to 1.

For y > e that is.
For y < e its even worse.

Since we are mainly intrested in small y and Large n ... This idea seems not so practical here.

Guess it might be more usefull for the base-change .... Well Maybe ...

Regards

Tommy1729
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Messages In This Thread
RE: Superroots and a generalization for the Lambert-W - by tommy1729 - 12/01/2015, 11:58 PM

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