Hi -

one remark at the beginning. I don't have another name than "powertower" for a singe tetration-term, so I still use this word here.

As you rememeber, at my initial interest were not the deep hardcore properties of the tetration-function, but rather some series, evaluated in my more general compilation of relations of important number-theoratical coefficients-matrices like binomials, stirling-numbers, bernoulli-numbers and the like (where tetration popped up as an iterative application)

I guess, it is of worth, to add to the knowledge-base also that pieces about series of tetration-terms, aka powertowers.

Here are two conjectures about identies of series; they are analogons to the known geometric series (if the tetration-exponent/iteration is 1 then the series are equal to geometric series). The first conjecture was already stated in different newsgroups.

They have a strange, but fascinating charme...

Gottfried

[update]: I adapted the title to improve the directory of the threads-list

one remark at the beginning. I don't have another name than "powertower" for a singe tetration-term, so I still use this word here.

As you rememeber, at my initial interest were not the deep hardcore properties of the tetration-function, but rather some series, evaluated in my more general compilation of relations of important number-theoratical coefficients-matrices like binomials, stirling-numbers, bernoulli-numbers and the like (where tetration popped up as an iterative application)

I guess, it is of worth, to add to the knowledge-base also that pieces about series of tetration-terms, aka powertowers.

Here are two conjectures about identies of series; they are analogons to the known geometric series (if the tetration-exponent/iteration is 1 then the series are equal to geometric series). The first conjecture was already stated in different newsgroups.

They have a strange, but fascinating charme...

Gottfried

[update]: I adapted the title to improve the directory of the threads-list

Gottfried Helms, Kassel