Discussion on "tetra-eta-series" (2007) in MO

[tommy1729]

In MO the user Caleb Briggs brings to discussion an old attempt of mine to the series \( T(x,2) = 1^{1^x} - 2^{2^x} + 3^{3^x} - \cdots + \cdots \) .
I've tried this on 2007, and only later learned some techniques with which I might have assessed this with more success. But my basic observations and also the computations that I'd been able to do (over a small range of the exponent \(x\) ) come out to be correct.      

For the friends of visual data - there are some nice pictures to see there.

Here is the link : 

https://mathoverflow.net/questions/43666...eta-series   

Here the link to my fiddlings:

http://go.helms-net.de/math/tetdocs/Tetra_Etaseries.pdf  

Have fun...

Gottfried

@James :

I meant splitting the positive and negative parts of  \( T(x,2) = 1^{1^x} - 2^{2^x} + 3^{3^x} - \cdots + \cdots \) and then using

 https://math.eretrandre.org/tetrationfor...p?tid=1688

my summability method on it.



regards

tommy1729