Heston-Nandi probability by recursion

Joined
6/25/13
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Hi everybody,
I need your help i'm working on my master thesis and my tutor ask me to develop the Pricing formula, but i don't understand how the authors find this formula.

In fact i don't understand how they find the P1 and P2 they say that they do it using a recursive way but they don't explain how.

If someone know and could help me.
Thanks a lot

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