Complex Analysis: Special Power Series

[nateHI]

Homework Statement

Give an example of a power series with [itex]R=1[\itex] that converges uniformly for [itex]|z|\le 1[\itex], but such that its derived series converges nowhere for $|z=1|[\itex].<br /> <br /> <h2>Homework Equations</h2><br /> R is the radius of convergence and the derived series is the term by term derivative.<br /> <br /> <h2>The Attempt at a Solution</h2><br /> I've tried a bunch of stuff but at the moment I'm leaning towards some variation of the power series for the sin function.<br /> It would be nice if there was a way to solve this without guessing and checking a bunch of times.$[/itex][/itex]

 

[nateHI]

It's OK to delete this. Posted it on accident.

 

[nateHI]

Sorry, I'm not sure why my latex commands aren't taking.

 

[BvU]

You want a forward slash to terminate, not a backslash.