Quick way to get the repelling fixed point from the attracting fixed point?

[JmsNxn]

Now to read up how to run W-Lambert. Skipped all those lessons, lmao.

(...)
This entirely solves the problem. But I don't know what branch of the Lambert function to use as of now.

Does anyone have a good formula for how the various branches of Lambert relate to the Lambert formula for the inverse of:

\[
g(y) = y^{1/y}\\
\]

Hmm, just to make sure: you know that LambertW (though without branch-index so far) is in Pari/GP? (I think in the 2.14-versions (alpha,experimental) they have it with branchindex) . And even better, the implementation in Pari/GP by our (former?) member mike4 - a real good one as it seems to me, allowing branch-indexing.

Gottfried

Hey, Gottfried.

All the pari-gp literature says that lambertW only works for the \(0\)-th branch on the real positive line. Are you saying I can call \(W_1\), because if I can call that in the complex plane, I'd dance around. That will save me fkn hours in CPU time, if it's just a taylor expansion built into pari.

Also, it was mike3, not mike4, who was the member here. I still use his graphing program....

Please tell me I can call:

\[
\frac{W_1(-\log(b))}{-\log(b)} = y\\
\]

Such that:

\[
|\log(y)| > 1
\]

And \(b = y^{1/y}\).

If you can point me to some pari-gp code which does this, Gottfried. THANK YOU!

I'll fucking s*** your d***

PLEASE TELL ME THIS IS POSSIBLE!!!