Author |
Topic: Power Series (Read 601 times) |
|
Braincramps
Newbie
Posts: 9
|
 |
Power Series
« on: May 12th, 2004, 2:27pm » |
 Quote  Modify
|
If f is a power series which converges at an endpoint of its interval of convergence, is f necessarily continuous at that endpoint?
|
|
 IP Logged |
|
|
|
TenaliRaman
Uberpuzzler
I am no special. I am only passionately curious.
Gender: 
Posts: 1001
|
|
Re: Power Series
« Reply #1 on: May 16th, 2004, 9:38am » |
Quote Modify
|
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)
|
| « Last Edit: May 16th, 2004, 1:24pm by TenaliRaman » |
IP Logged |
Self discovery comes when a man measures himself against an obstacle - Antoine de Saint Exupery
|
|
|
|
RIDDLES SITE
WRITE MATH!
Home 
Help 
Search 
Members 
Login 
Register
Reply
Notify of replies
Send Topic
Print