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Simple question on expansion

  1. May 7, 2016 #1
    1. The problem statement, all variables and given/known data
    I am trying to expand [itex]\frac{1}{(1+\frac{a^2}{z^2})^{1/2}}[/itex] for z>>a.

    2. Relevant equations


    3. The attempt at a solution
    First, I rearranged the equation to [itex](1+\frac{a^2}{z^2})^{-1/2}[/itex]. After this, since z>>a, can I assume z takes a value of infinity and say the first term is 1+0=1? And I am not sure what to do for the second term. I take the first derivative which is [itex]-\frac{1}{2}(1+\frac{a^2}{z^2})^{-3/2}(\frac{-2a^2}{z^3})[/itex] and not sure what to do with it.
    Any help will be appreciated.
     
  2. jcsd
  3. May 7, 2016 #2

    Ray Vickson

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    So, are you not just trying to expand ##(1 + x^2)^{-1/2}## for small ##x = a/z##?
     
  4. May 7, 2016 #3
    I'm having difficulty understanding how to expand for small x. I've only come across questions that ask something like "expand this function around x= some number". Do I take x=0?

    EDIT: Ah, so do I take x=0 and is the second non-zero term the term using second derivative?
     
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