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Taylor Series Expansion

  • Thread starter Applejacks
  • Start date
  • #1
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Homework Statement



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

Homework Equations





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:

Answers and Replies

  • #2
Dick
Science Advisor
Homework Helper
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They are exactly the same thing. The first expression is just the first two terms of the second.
 
  • #3
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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
 
  • #4
Dick
Science Advisor
Homework Helper
26,258
618
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
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.
 
  • #5
33
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ah right. Thanks for pointing that out.
 

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