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Well defined Power Series

IsThisIt??? · 2011-08-08 01:57:24

I found a question where you are asked to verify that the power series exp(x) is well defined. I have no idea how to do this. I understand how to show basic functions are well defined or not but don't even know where to start with this....

08-08-2011 1:57am

#1

IsThisIt???

Registered Users, Registered Users 2 Posts: 412 ✭✭

Join Date: November 2009

Posts: 347

I found a question where you are asked to verify that the power series exp(x)
is well defined. I have no idea how to do this.

I understand how to show basic functions are well defined or not but don't even know where to start with this....

0

Comments

#2 08-08-2011 11:05am

Fremen

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Join Date: May 2006

Posts: 2356

Just show that it's absolutely convergent for every real number.

If a series is conditionally convergent, then it's not necessarily well defined since you also have to specify an order in which to sum the terms. On the other hand, absolutely convergent series are unambiguous.

0