1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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:

    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


    User Avatar
    Science Advisor
    Homework Helper

    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


    User Avatar
    Science Advisor
    Homework Helper

    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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook