andydude Wrote:Here is the power series that corresponds to regular iteration:Hmm, now I see first time the difference... (why not start one thread "Basics" and add (or reference) posts to these basic questions - it may be easier to add information than to add to a mega-document Tex-Faq)

And here is the power series that corresponds to natural iteration:

Concerning the second: my coefficients for the eigensystem-based analysis shows, that the series w.r.t height t (or h) have t in the exponent; they are *not* powerseries (except for one set of bases), so I wonder, whether the above formal derivative is correct?

[update] hmm, on a second read I may answer this by myself: this difference is coded in the different type of derivatives [D...] only - the taylor formula is true for any type of series.

But there is still one aspect, which I'll think about. Conversion of a zeta-series (the parameter is in the exponent, similar to the expansion of It. dec. exp.) into a representation as a powerseries involves the mystic stieltjes-constants, which are related to the euler-mascheroni-constant gamma. [/update]

Gottfried

Gottfried Helms, Kassel