In Reply to: Question about HW5 Q2e posted by Josh on May 08, 2003 at 16:39:24:
Nevermind, don't answer this question, I see what's wrong with my argument.
>Hello,
>Q2e asks to find a power formal power series centered at 0 with radius 1 such that it converges pointwise on (-1,1) but not uniformly on (-1,1).
>According to Theorem 12c - uniform convergence on compacta - For any 0 < r < R the series converges uniformly to some function f on the compact interval [a-r,a+r].
>Using this, then for any epsilon>0 , the series converges uniformly on the interval [-1+epsilon,1-epsilon] so the series is uniformly convergent over any closed interval in (-1,1), therefore there does not exist any such series?
>I'm writing this because I'm having trouble finding the series and i wish it didn't exist. Thanks
>Josh