1. Apr 15, 2009 #1

   captainjack2000

   

   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

    

   captainjack2000, Apr 15, 2009
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3. Apr 15, 2009 #2

   latentcorpse

   

   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]

    

   latentcorpse, Apr 15, 2009

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