Statistical moments and multipole moments

[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.

 

[Almsco]

Hi there,

I'm not sure if there is a similar method to deriving the multipole moments in electrodynamics using a generating function as with statistics. I think the multipole moments are derived from the expansion of \frac {1}{\left|x\right|} because this is a measure of the electric field at a given point, which is related to the multipole moments. Have you tried researching this further? Maybe someone else on the forum may have more information on this topic that can help provide more insight.