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Statistical moments and multipole moments

  1. Jun 7, 2009 #1

    in statistics, one can derive the moments of a distribution by using a generating function
    [tex]<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}[/tex]

    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
    [tex]\frac {1}{\left|x\right|}[/tex]
    but I don't seem to get the connection to a generating function.
  2. jcsd
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