Talk:Mathematical Methods of Physics/The multipole expansion

Possible error

Should:

$$\frac{1}{\left|1-2\frac{\hat{\mathbf{r}}\cdot\mathbf{r}'}{r}+\left(\frac{r'}{r}\right)^2\right|^{\frac{1}{2}}}=1-\frac{\hat{\mathbf{r}}\cdot\mathbf{r}'}{r}+\frac{1}{2r^2}\left(3(\hat{\mathbf{r}}\cdot\mathbf{r}'\right)^2-r'^2)+O\left(\frac{r'}{r}\right)^3$$

be:

$$\frac{1}{\left|1-2\frac{\hat{\mathbf{r}}\cdot\mathbf{r}'}{r}+\left(\frac{r'}{r}\right)^2\right|^{\frac{1}{2}}}=1+\frac{\hat{\mathbf{r}}\cdot\mathbf{r}'}{r}+\frac{1}{2r^2}\left(3(\hat{\mathbf{r}}\cdot\mathbf{r}'\right)^2-r'^2)+O\left(\frac{r'}{r}\right)^3$$