# Multipole expansion

1. Dec 10, 2008

### h0dgey84bc

Hi,

I'm just working through some electrodynamics notes, and am a bit stuck following a particular Taylor expansion, the author starts with:

$\frac{1}{R_1}=\frac{1}{r} [1+(\frac{l}{r})^2-2\frac{l}{r}cos(\theta)]^-0.5$

Which he then says by assuming l<<r and expanding we get:

$\frac{1}{R_1}=\frac{1}{r} [1+(\frac{l}{r})cos(\theta)+\frac{1}{2}(\frac{l}{r})^2(3cos(\theta)^2-1)+ \frac{1}{2}(\frac{l}{r})^3(5cos(\theta)^2-3cos(\theta)) ]....$

Just a bit lost at how to do this, what variables am I expanding wrt?

thanks

2. Dec 10, 2008

### clem

The variable u=(L/r)

3. Dec 11, 2008

thanks clem