I've deleted most of the messages about this. Can someone repeat the Hardy references that were given in one message? Was there a page number given for Divergent Series? R. On Wed, 18 May 2005, Gareth McCaughan wrote:
On Wednesday 18 May 2005 19:33, dasimov@earthlink.net wrote:
This is exactly the proof supplied by Noam Elkies, who includes the problem as #8 with some other cute problems and tidbits at http://www.math.harvard.edu/~elkies/Misc/. The given solution includes a nice graphic that can be zoomed in upon near x = 1.
So. Call an infinite set of non-negative integers "good" if the alternating power series F constructed from it in the same way has lim { x -> 1 from below } F(x) existing. We've established that the powers of 2 aren't good. It's well known that the full set of positive integers is good; the limit is 1/2.
Which sets are good? Can the limit exist but not be 1/2?
-- g
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun