# Homework Help: PDE Series Problem

1. Jan 28, 2012

### Airsteve0

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
$a_{n+2}$=($\frac{n(n+3)-\lambda}{R^{2}(n+2)(n+3)}$)$a_{n}$ -> assume $a_{o}$=1

$\lambda$=$\frac{2m^{2}}{\omega_{o}^{2}}$ -> m is the separation constant

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

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