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Taylor expansion

  1. Apr 15, 2009 #1
    1. The problem statement, all variables and given/known data
    Could someone please explain how the taylor expansion of 1/(r-r') turns into
    ( 1/r+(r'.r)/r^3 + (3(r.r')^2-r^2r'^2)/2r^5 +...)


    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Apr 15, 2009 #2
    i think it should be [itex]\frac{1}{|\vec{r}-\vec{r'}|}[/itex] yes?

    use the 3d taylor expansion formula

    [itex]\phi(\vec{r}+\vec{a})=\sum_{n=0}^{\infty} \frac{1}{n!} (\vec{a} \cdot \nabla)^n \phi(\vec{r})[/itex] with [itex]\phi(\vec{r}+\vec{a})=\frac{1}{|\vec{r}-\vec{r'}|}[/itex]
     
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