(10/31/2009, 02:40 PM)Gottfried Wrote: Check, for base x=1/2 I get AS(x) = 0.938253002500

Yes, with the average of the two series, I get AS(0.5) = 0.938253.

The way that I got the coefficients is slightly different than your method. I did this:

Let be a matrix defined by , and let

then

so I thought, if we know G (1, -1, 1, -1, ...), then

and when the matrix size is even I get the first series, and when the matrix size is odd, I get the second series.