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Homework Help: Power Series

  1. May 22, 2005 #1
  2. jcsd
  3. May 22, 2005 #2

    dextercioby

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    It doesn't converge for every possible "x",as your "radius of convergence =infinite" might mean.

    [tex] \sum_{k=1}^{\infty} (-1)^{k}\frac{x^{2k}}{4^{k}(k!)^{2}} =-\frac{x^{2}}{4}\ _{2}F_{1} \left(1,2,2;-\frac{x^{2}}{4}\right) [/tex]


    Daniel.
     
  4. May 22, 2005 #3
    To simplify
    there was no need to take the x's ...take x^2=w and just take the limit of the ratio's..

    As per my knowledge it seems to me R is infinite
     
  5. May 22, 2005 #4

    dextercioby

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    Well,try x=60.How big is the number...?

    Daniel.
     
  6. May 23, 2005 #5
    Thanks for the replies guys.

    I have left it as R = infinity; seems the rest of the class got the same thing. So I'll just leave it at that
     
  7. May 23, 2005 #6

    shmoe

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    You've missed the k=0 term, though this doesn't affect convergence. The OP's work is fine.

    For interests sake, this thing is a Bessel function of the first kind (it's a solution to the d.e. xy''+y'+xy=0).
     
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