06/14/2011, 04:22 AM
(06/08/2011, 11:47 PM)JmsNxn Wrote: However, I am willing to concede the idea of changing from base eta to base root 2.
That is to say if we define:
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This will give the time honoured result, and aesthetic necessity in my point of view, of:
for all
.
I like this also because it makesand
potentially analytic over
since 2 and 4 are fix points.
I also propose writing
I thought about this for some time and considered interpolation between arithmetic mean and geometric mean, coming to a rather curious result. The 'mean' function with
Define
For
So it's not a 'true mean' in the sense that the scalar multiplication property fails. This result makes me doubt that the property may be satisfied for