Taylor expansion

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

latentcorpse

i think it should be [latex]\frac{1}{|\vec{r}-\vec{r'}|}[/latex] yes?

use the 3d taylor expansion formula

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

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captainjack2000	Taylor expansion 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

latentcorpse	i think it should be [latex]\frac{1}{\|\vec{r}-\vec{r'}\|}[/latex] yes? use the 3d taylor expansion formula [latex]\phi(\vec{r}+\vec{a})=\sum_{n=0}^{\infty} \frac{1}{n!} (\vec{a} \cdot \nabla)^n \phi(\vec{r})[/latex] with [latex]\phi(\vec{r}+\vec{a})=\frac{1}{\|\vec{r}-\vec{r'}\|}[/latex]