Algebraic substitution

  1. cristo

    cristo 8,412
    Staff Emeritus
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    1. The problem statement, all variables and given/known data

    I have this function [tex]F(r)=\frac{(r-r_+)(r-r_-)}{r^2}[/tex] and I want to make the subsitution [itex]r=r_+(1+\rho^2)[/itex].
    2. Relevant equations

    None.

    3. The attempt at a solution

    So, I sub in, to obtain [tex]F=\frac{[r_+(1+\rho^2)-r_-][r_+(1+\rho^2)-r_-]}{r_+^2(1+\rho^2)^2}=\frac{\rho^2[r_+(1+\rho^2)-r_-]}{r_+^2(1+\rho^2)^2}[/tex].

    Now, the solutions say that this is equal to [tex]\frac{r_+\rho^2(r_+-r_-)}{r_+^2}\cdot [1+O(\rho^2)] [/tex], however I cannot, for the life of me, see how to get this from my line above! Can anyone help?
     
  2. jcsd
  3. Hootenanny

    Hootenanny 9,678
    Staff Emeritus
    Science Advisor
    Gold Member

    Looks like a Taylor expansion to me, but I could be wrong...
     
  4. cristo

    cristo 8,412
    Staff Emeritus
    Science Advisor

    Yup, you're correct. I never spot things like that. Thanks! :smile:
     
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