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Taylor Series Expansion

  1. Oct 27, 2011 #1
    1. The problem statement, all variables and given/known data

    Find the Taylor series expansions for f(z) = −1/z^2 about z = i + 1.

    2. Relevant equations



    3. The attempt at a solution

    I'm just not sure what format I'm supposed to leave it in.

    Is it meant too look like this:
    f(z)=f(i+1)+f'(i+1)(x-i-1)...

    or this
    Ʃ[itex]\frac{1}{n!}[/itex][itex]f^{(n)}[/itex](1+i) * (z-i-1)^n (also is this correct?)
     
    Last edited: Oct 27, 2011
  2. jcsd
  3. Oct 27, 2011 #2

    Dick

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    They are exactly the same thing. The first expression is just the first two terms of the second.
     
  4. Oct 27, 2011 #3
    Yeah I'm aware of that. I guess I should keep it in the second form though. Another question: what does the square do to the function. What I wrote can't be correct because -1/z would give the same thing.

    Ʃ[itex]\frac{1}{n!}[/itex][itex]f^{(n)}[/itex](1+i) * (z-i-1)^2n
     
  5. Oct 27, 2011 #4

    Dick

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    What?? Changing f changes f^(n)(i+1). That changes the series doesn't it? The power part (z-i-1)^n doesn't change. Those are the powers in the expansion of any function around i+1.
     
  6. Oct 27, 2011 #5
    ah right. Thanks for pointing that out.
     
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