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Understanding an expansion into a geometric series

  1. Oct 23, 2014 #1
    Hi all,

    I am reading through Riley, Hobson, and Bence's Mathematical Methods for Phyisics and Engineering, and on page 854 of my edition they describe (I am replacing variables for ease of typing)

    "expanding 1/(a-z) in (z-z0)/(a-z0) as a geometric series 1/(a-z0)*Sum[((z-z0)/(a-z0))^n] for n = 0 to infinity."

    I looked up the Taylor expansion of 1/(1-x) and see that it has a geometric form (Sum[x^n] also from 0 to infinity), but I do NOT see how or why they are introducing z0. Can someone explain explicitly what's going on here?

    Much thanks!
  2. jcsd
  3. Oct 25, 2014 #2


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    Science Advisor

    It looks like the authors wanted the students to learn how to get Taylor series around points other than 0.
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