Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Algebraic substitution

  1. May 13, 2007 #1

    cristo

    User Avatar
    Staff Emeritus
    Science Advisor

    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. May 13, 2007 #2

    Hootenanny

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Looks like a Taylor expansion to me, but I could be wrong...
     
  4. May 13, 2007 #3

    cristo

    User Avatar
    Staff Emeritus
    Science Advisor

    Yup, you're correct. I never spot things like that. Thanks! :smile:
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Similar Discussions: Algebraic substitution
  1. Integral substituting (Replies: 4)

  2. Substitution for DE (Replies: 1)

Loading...