# Statistical moments and multipole moments

1. Jun 7, 2009

### Meta Mass

Hello,

in statistics, one can derive the moments of a distribution by using a generating function
$$<x^n> = \int dx x^n f(x) = \left( \frac {d}{dt} \int dx \exp(tx) f(x) \right)_{t=0} = \left( \frac d {dt} M(t) \right)_{t=0}$$

Is there a similar method to derive the multipole moments in electrodynamics, e.g. is there a generating function? I know that the multipole moments are derived from the expansion of
$$\frac {1}{\left|x\right|}$$
but I don't seem to get the connection to a generating function.