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Potential series method

  1. Dec 19, 2012 #1
    Why sometimes we search solution of power series in the way:
    [tex]y(x)=\sum^{\infty}_{n=0}a_nx^n[/tex]
    and sometimes
    [tex]y(x)=\sum^{\infty}_{n=0}a_nx^{n+1}[/tex]???
     
  2. jcsd
  3. Dec 20, 2012 #2

    tiny-tim

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    hi matematikuvol! :smile:
    no particular reason …

    sometimes one gives neater equations than the other …

    they'll both work (provided, of course, that y(0) = 0) :wink:
     
  4. Dec 21, 2012 #3
    I think that in the case when
    [tex]\alpha(x)y''(x)+\beta(x)y'(x)+\gamma(x)y(x)=0[/tex]
    if ##\alpha(0)=0## you must work with ##\sum^{\infty}_{n=0}a_nx^{n+k}##, but I'm not sure.
     
  5. Dec 21, 2012 #4

    tiny-tim

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    but that's the same as ##\sum^{\infty}_{n=0}b_nx^n## with ##b_n = a_{n-k}## for n ≥ k, and ##b_n = 0## otherwise :wink:
     
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