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Non analytic function?

  • Thread starter rcmbimp
  • Start date
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Non analytic function???

1. Homework Statement

I was set this question as part of an extra problem sheet by my maths teacher, and i dont know where to start. He said its like first year university maths standard, and gave me hints to use the maclaurins and binomial series. Im just a bit stuck... PLEASE HELP... I found an example of a non analytical function on this forum, but just confused me!

the question...

Consider the function
f(x) = "e− 1
x2 if x "= 0
0 if x = 0
.
Calculate the Maclaurin series of f and show that it does not converge to f(x) for x "= 0. In
particular f is not an analytic function.

2. Homework Equations

Maclaurins series
Binomial expansion

3. The Attempt at a Solution

I dont know where to start
 

Astronuc

Staff Emeritus
Science Advisor
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woops... cant copy and paste!

Yes sorry it is an e^x....

Thanks for yuor reply, but im still really stuck. I emailed my teacher the other day and he said to try find an example, and just understand it (or try to understand it).

Does anyone know where i could find a worked solution of this... preferablely with quotations as it goes along...

thanks
rcmbimp
 

Astronuc

Staff Emeritus
Science Advisor
18,547
1,682
Yes sorry it is an e^x....

Thanks for yuor reply, but im still really stuck. I emailed my teacher the other day and he said to try find an example, and just understand it (or try to understand it).

Does anyone know where i could find a worked solution of this... preferablely with quotations as it goes along...
This page has some good examples regarding convergence of a series.
http://www.math.ubc.ca/~indurskis/math100/taylor/example6.html [Broken]

Think about the purpose of expanding using a series and then think about the criterion for convergence.
 
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