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[AIS] (alternating) Iteration series: Half-iterate using the AIS?

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[AIS] (alternating) Iteration series: Half-iterate using the AIS?
Gottfried Offline
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12/15/2012, 06:49 AM
(12/15/2012, 04:47 AM)sheldonison Wrote: Gottfried,

This new superfunction is intriguing to me, so I generated a Taylor series for it. This alternating sum function seems to be clearly a different solution than anything we've seen before, and it is analytic in the complex plane.

Hi Sheldon -

this sounds really great; at the moment (saturday morning, 7 o'clock) it's a bit over my head, but I'll come back to it later. Cool, that you already did the view into the complex plane, that is all much curious...

What about the cosine instead of the sine? You introduced the cosine in the formula: is there some optimization argument for it? I think it shifts the height-zero-definition from \( x_0 \) to the \( x_{0.5} \) -position and must be compensated elsewhere in the formulae?

Gottfried
Gottfried Helms, Kassel
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RE: Iteration series: Half-iterate using the infinite iteration-series? - by Gottfried - 12/15/2012, 06:49 AM

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