Complex Analysis: Special Power Series

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Homework Help Overview

The original poster attempts to find an example of a power series with a radius of convergence of 1 that converges uniformly for |z| ≤ 1, but whose derived series converges nowhere on the boundary |z| = 1. The subject area is complex analysis, specifically focusing on power series and their properties.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • The original poster mentions trying various approaches, particularly considering a variation of the power series for the sine function. They express a desire for a more systematic method rather than relying on trial and error.

Discussion Status

The discussion is ongoing, with participants exploring different aspects of the problem. Some guidance has been offered regarding the use of LaTeX commands, but no consensus or resolution has been reached regarding the main question.

Contextual Notes

There are indications of technical issues with formatting in the posts, which may affect the clarity of the discussion. The original poster's approach appears to involve assumptions about the properties of power series and their derivatives.

nateHI
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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 [itex]|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][/itex]
 
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It's OK to delete this. Posted it on accident.
 
Last edited:
Sorry, I'm not sure why my latex commands aren't taking.
 
You want a forward slash to terminate, not a backslash.
 

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