Multi Dimensional PVN

[Gottfried]

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Hmm, did you know that in 2007 I proposed a summation for the series
\( a_{10}(2) = 2 - 10^2 + \text{googol} - \text{googolplex} + 10^{\text{googolplex}} - ... + ... \approx 0.336339355 \)
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Gottfried

How do you calculate the sum of this super-exponentially growing alternating series?

It is a conjecture because some convergence in the required matrix-formula was only observed for truncated matrices but I could not prove them.
Here is the initial article of 2007 (which is much amateurish since I was just entering the field of tetration) http://go.helms-net.de/math/tetdocs/10_4...rticle.pdf ; later I did a conversation in sci.math.research to improve the plausibility of the results, I've collected that discussion at http://go.helms-net.de/math/tetdocs/Iter...tion_1.htm .

Gottfried