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Iteration basics
#11
andydude Wrote:Here is the power series that corresponds to regular iteration:


And here is the power series that corresponds to natural 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)

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
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Messages In This Thread
Iteration basics - by Ivars - 03/20/2008, 10:34 AM
RE: Iteration basics - by Ivars - 03/20/2008, 05:24 PM
RE: Iteration basics - by Gottfried - 03/21/2008, 08:37 AM
RE: Iteration basics - by Ivars - 04/03/2008, 08:05 AM
RE: Iteration basics - by Gottfried - 04/03/2008, 08:19 AM
RE: Iteration basics - by Ivars - 04/03/2008, 10:13 AM
RE: Iteration basics - by andydude - 04/05/2008, 11:35 PM
RE: Iteration basics - by Gottfried - 04/06/2008, 07:16 AM
RE: Iteration basics - by Ivars - 04/06/2008, 08:55 AM
RE: Iteration basics - by andydude - 04/07/2008, 12:01 AM
RE: Iteration basics - by Ivars - 04/20/2008, 10:15 PM
RE: Iteration basics - by bo198214 - 04/21/2008, 08:21 PM
RE: Iteration basics - by andydude - 04/22/2008, 05:30 AM
RE: Iteration basics - by Ivars - 04/22/2008, 07:02 AM
RE: Iteration basics - by Ivars - 04/09/2008, 07:56 PM
RE: Iteration basics - by Ivars - 05/09/2008, 09:45 AM
RE: Iteration basics - by bo198214 - 05/09/2008, 02:49 PM
RE: Iteration basics - by Ivars - 05/27/2008, 10:33 AM
RE: Iteration basics - by Gottfried - 05/27/2008, 07:35 PM
RE: Iteration basics - by Ivars - 05/30/2008, 06:08 AM
RE: Iteration basics - by Xorter - 01/02/2017, 05:21 PM

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