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- Jun 20, 2014

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Let $q$ be a complex number with $\lvert q \rvert < 1$. Show that

$$\prod_{n = 1}^\infty (1 - q^n) \sum_{n = -\infty}^\infty q^{n+2n^2} = \prod_{n = 1}^\infty (1 - q^{2n})^2$$

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**Note**: Do not worry about arguments of convergence.

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