Hello there, I was having some trouble with this problem:

Find the Taylor series for f centered at 4 if:

What is the radius of convergence of the Taylor series?

Help appreciates.

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- Nov 17th 2011, 11:40 PMIntrusionFinding Taylor series for f
Hello there, I was having some trouble with this problem:

Find the Taylor series for f centered at 4 if:

What is the radius of convergence of the Taylor series?

Help appreciates. - Nov 18th 2011, 12:37 AMalexmahoneRe: Finding Taylor series for f
- Nov 18th 2011, 04:44 AMchisigmaRe: Finding Taylor series for f
- Nov 18th 2011, 10:38 PMFernandoRevillaRe: Finding Taylor series for f
The problem is ill defined, we have no sufficient information about . For example

We have . However: a) The Taylor series of centered at has radius of convergence . b) The Taylor series of centered at does not exist . - Nov 19th 2011, 02:07 AMchisigmaRe: Finding Taylor series for f
May be that a further explanation from me is necessary... if we consider the series expansion...

(1)

...it is not too difficult to obtain...

(2)

Now the f(*) defined in (2) is analytic for and that means that its series expansion centered in has radius of convergence ...

Kind regards

- Nov 19th 2011, 02:48 AMFernandoRevillaRe: Finding Taylor series for f