12/30/2015, 09:49 AM

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 .

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 .