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Hm, please excuse my lack of creativity when searching for a nice term for the subject ;-)

Anyway, I've uploaded a small treatise about infinite series of towers of like height (here of height 2) with concecutive increasing *bases* (remember, that my recent conjectures had the same bases, but increasing top-exponent)
It may be interesting as a step into unknown area - I don't arrive at a special conjecture. But may be some other has an idea?

I have it only as a pdf-file here; well besides the attachment I better add the url in case that I have to extend the article.
It is at Tetra_Etaseries.pdf


Gottfried
Though I have no good idea about your topic,
I really would appreciate attaching every document.
Because this forum is meant also to be an archive and to still exist if every other web page is declined already Wink
And it would be a pitty if one could not read articles anymore because the original URLs are no more existing or were moved.
bo198214 Wrote:Though I have no good idea about your topic,
I really would appreciate attaching every document.
Because this forum is meant also to be an archive and to still exist if every other web page is declined already Wink
And it would be a pitty if one could not read articles anymore because the original URLs are no more existing or were moved.

Hi Bo, nice to read you again!

Well, I detached my initial attachment due to frequent changes in a single day... If the text is stable, it's ok to reattach it - yes, the stability of URL's is really a problem...

For the contents of the article. One problem to solve is to get bounds for the sums of powers of logarithms, the lambda-function. Although the graph suggests strongly that the scaling |asinh(lambda(x))/x| approaches asymptotically a constant bound and approximates it llocally relatively early I don't have an idea, how this could be settled. (the other problems may be approached later ;-)

Gottfried