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- Jun 24th 2011, 09:47 AMKrizalidA limit
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- Jun 24th 2011, 10:40 AMTKHunnyRe: A limit
Just toying with it a bit, I note:

n = 4 results in something between 1 and 2 half-periods

n = 7 results in something between 2 and 3 half-periods

n = 13 results in something between 4 and 5 half-periods

n = 26 results in something between 8 and 9 half-periods

Seems like this could lead somewhere useful, at least getting bounds on it. - Jun 24th 2011, 03:05 PMTKHunnyRe: A limit
Okay, I haven't quite talked myself into it, yet, but let's see how far it gets me.

For an arbitrary 'n', the half period is . If we restrict the evaluation of the integral to the first half period, the Absolute Values become unnecessary.

Given the half-period of , quite obviously there are such half periods in [0,1].

Somewhat to my surprise, this makes the result independent of 'n'.

It's not obvious what I'm missing. Clearly, the limit it greater than that, but I figured I'd get it out there for ridicule. - Jun 24th 2011, 06:50 PMKrizalidRe: A limit
is the answer.

- Jun 24th 2011, 08:06 PMTKHunnyRe: A limit
Hmmm...Maybe I was looking at rounding error, but I definitely exceeded that in numerical examples.

Some other way to get there? - Jun 25th 2011, 02:51 AMDrexel28Re: A limit
- Jun 25th 2011, 03:23 PMArchie MeadeRe: A limit