Iteration series: Series of powertowers - "T- geometric series"

[Gottfried]

... Here are two conjectures about identies of series;.. Gottfried

1. Gottfried: Your "here" leads to
http://go.helms-net.de/math/pdf/Tetratio...ort.pdf%20
causing diagnistics

Not Found
The requested URL /math/pdf/Tetration_GS_short.pdf was not found on this server.

Could you check it please?

There is a trailing blank in your link. To access the file please just remove that trailing link in the address-field of your browser. I'll also repair that link in my index-page. Thanks for the notification!
The link is http://go.helms-net.de/math/pdf/Tetration_GS_short.pdf


Also, perhaps I should update that old file with my new knowledge:

a) The conjectures for series of powertowers of height greater than 1 were shown to be not true by some correspondent.
However, that concerns only one half of the doubly infinite series: either the series with indexes k = 0 to -infinity or that with k=0 to + infinity is wrong using the matrix-method and the other is correct.
Moreover, my suspection is that the error is systematic and possibly can be compensated by some term similar to the procedure which we know from the Ramanujan-summation, where we need to consider one additional integral-expression for the validity of the divergent Ramanujan-summation. But I did not find yet an appropriate expression for this in the case of the iteration-series of powertowers/tetration.

b) Some things could now be expressed less exploratory and hypothetical and instead more formal and firm.

I'll see what i can do at the weekend...

Gottfried