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Could you explain me the last equality in the proof? I mean this:

$$\frac{2[\sqrt{1 - s^2t^2} - \sqrt{1-t^2}]}{t^2(1-s^2)} = \sum_{n=0}^{\infty} t^{2n} P(S_{2n} = 0) \left(\frac{1 - s^{2n+2}}{(n+1)(1-s^2)}\right)$$

Thank you very much in advance.

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You have posted this simultaneously on math.stack exchange, which is the appropriate place for it. If you read the faq for this site (the link's at the top of this page) you will see why it does not belong here. – Chris Godsil Jan 15 '13 at 0:36
Oh, I'm sorry for the mistake. Indeed this is not the appropriate place. Now I know where I should ask about what kinds of problems ;) Best regards, – user58302 Jan 15 '13 at 1:56

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