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Superroots and a generalization for the Lambert-W
#23
I believe I may have found a closed form for the power series of the third tetrate function as well.
I'm not sure if these are known, but I just used the elementary properties of binomials and Stirling numbers to derive these:





The first one (logarithmic power series) reminds me of something in one of Galidakis' papers about tetration, but I don't remember which paper. The second one is derived from the fact that the generating function of the signed Stirling numbers the first kind is .
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RE: Superroots and a generalization for the Lambert-W - by andydude - 12/30/2015, 09:49 AM

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