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        riddles >> putnam exam (pure math) >> Power Series
        
(Message started by: Braincramps on May 12^th, 2004, 2:27pm)

Title: Power Series
Post by Braincramps on May 12^th, 2004, 2:27pm

If f is a power series which converges at an endpoint of its interval of convergence, is f necessarily continuous at that endpoint?

Title: Re: Power Series
Post by TenaliRaman on May 16^th, 2004, 9:38am

i think the definition of continuity answers this one easily.
We know that we require this condition,
limx->a- = lim x->a+ = f(a)

and the a's in question in this case are the endpoints of an interval, so obviously it need not be continuous.

the above is an example of bad math gone rotten.i really need to re-read those complex analysis books.

As for the question yes it is continuous at the "endpoints".
(emphasizing endpoints since that is where i messed up in my earlier post)