Representing a function as a power series

  • Thread starter grothem
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  • #1
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Homework Statement


Evaluate the indefinite integral as a power series and find the radius of convergence

[tex]\int\frac{x-arctan(x)}{x^3}[/tex]


I have no idea where to start here. Should I just integrate it first?

Homework Statement





Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #2
Dick
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Sure, you could do that. But, I think what they want to do is expand arctan(x) as a power series around 0 and then integrate.
 
  • #3
23
1
ok. So arctan(x) = [tex]\int\frac{1}{1+x^2}[/tex]
= [tex]\int\sum (x^(2*n))[/tex]
= [tex]\sum\frac{x^(2(n+1)}{2(n+1)}[/tex]

is this what you mean?
 
  • #4
Dick
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That's one way to get a series for arctan, yes. But you forgot a (-1)^n factor. The expansion of 1/(1-x) has all plus signs. 1/(1+x) doesn't.
 

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