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Math Help - Bessel Identity as a power seriers

  1. #1
    Junior Member
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    Bessel Identity as a power seriers

    Hello,

    Im trying to arrange

    J_0(x) + \sum^{infnty}_{n=1} J_n(x) (r^n+{(-1)}^nr^{-n})

    into a power series.

    I've attempted but cannot get it into the form required. I've tried subbing in the series representation of J_n(x) into it.

    Any advice would be very helpful. Thanks
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  2. #2
    Super Member girdav's Avatar
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    Re: Bessel Identity as a power seriers

    You want a power series with respect to r, right? So you are looking in fact for Laurent series.
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