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PDE Series Problem

  1. Jan 28, 2012 #1
    1. The problem statement, all variables and given/known data
    The problem I am having has to do with part (d) in the picture which I have attached. I have managed to get as far as to determine that the coefficients in the series expansion have the recurrence relation shown below in part (2). From this I think that I have been able to determine that the general form of the coefficients must what is shown in part (3) below. The issue is I am unsure of how to get the proper form of the numerator. Any assistance would be greatly appreciated, thanks!


    2. Relevant equations
    [itex]a_{n+2}[/itex]=([itex]\frac{n(n+3)-\lambda}{R^{2}(n+2)(n+3)}[/itex])[itex]a_{n}[/itex] -> assume [itex]a_{o}[/itex]=1

    [itex]\lambda[/itex]=[itex]\frac{2m^{2}}{\omega_{o}^{2}}[/itex] -> m is the separation constant

    3. The attempt at a solution
    [itex]a_{2n}[/itex]=[itex]\frac{something}{(R^{2})^{n}(2n+1)!}[/itex]
     

    Attached Files:

  2. jcsd
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