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Power series, x=0

  1. Nov 16, 2011 #1
    what does it mean if y(x)=[itex]\sum[/itex][itex]^{∞}_{n=0}[/itex] an(x-x0)n
    and y(0)=1 ?
    does this mean that x0=0 and a0=1 ?
     
  2. jcsd
  3. Nov 16, 2011 #2

    lurflurf

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    Homework Helper

    It means y(0)=1.

    That x0=0 and a0=1

    is one (obvious) possibility, but sometimes other choices are used.

    For example we might chose a different x0 is there is a singularity near zero and we need the series to converge is a certain range. Like if there were a singularity at x=-1 and we would like a series valid on (-1,3) we might choose x0=2. Then y(0)=1 means

    1=y(0)=[itex]\sum[/itex][itex]^{∞}_{n=0}[/itex] an(-2)n

    A bit tricky to work with, but not too bad.
     
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