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?(x) convolved with a gaussian again

🔗Mike Battaglia <battaglia01@gmail.com>

1/31/2011 4:54:56 AM

OK, uploaded some more files:

/tuning-math/files/MikeBattaglia/%3F%28x%29%20convolved%20with%20g%28x%29/

I also tried convolving ?(2^x)/2^x, which straightened out the curve,
but shifted the minima down by a little bit. The results look very
similar to what happened when I tried to seed the HE calculation with
the Stern-Brocot tree, which might stem from the fact that there's a
connection between ?(x) and the SB tree to begin with.

So in light of this, some pertinent questions are:

1) Is ?(x) the measure of width that you get if you take the limit of
the distribution of the Stern-Brocot numbers out to infinity?
2) If not, could some series be constructed that approaches ?(x) as a
measure of width as the series approaches the infinite case?
3) Could some function analogous to ?(x) be constructed that
represents the measure of width for the Farey and Tenney series?

If the latter point turns out to be true then we'd have the fastest HE
algorithm possible, I think.

-Mike