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Cumulant expansion

  1. Jun 7, 2015 #1
    Can anyone tell me how a cumulant expansion, like the one on the picture, works? If I take the logarithm of the expansion in eq. (29-26) I don't get what is stated below. What should I do to get that?
     

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  2. jcsd
  3. Jun 7, 2015 #2

    Svein

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    I also don't agree with the transfer from (29-26) to (29-27). Either there is something very wrong with the statement or there is something going on backstage that we are not shown.
     
  4. Jun 7, 2015 #3
    You need to verify that the derivatives of ##\log(G(k))## evaluated at ##k=0## are exactly the Ξr
    For example: ##\frac{d}{dk}\log(G(k)) = \frac{G^\prime(k)}{G(k)}##. Remember that ##G(0) = 1## and ##G^\prime(0) = <Y>##. Hence the derivative evaluated at ##0## is ##<Y>##, as desired. I will let you compute the other Ξr.
     
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