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Gauss came up with some bizarre identities, namely $$ \sum_{n\in\mathbb{Z}}(-1)^nq^{n^2}=\prod_{k\geq 1}\frac{1-q^k}{1+q^k}. $$

How can this be interpreted combinatorially? It strikes me as being similar to many partition identities. Thanks.

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    The first one (at least the $q^{n^2}$ part) just says that the divisors of a non-square can be divided into pairs $\{a,b\}$ such that $ab=1$. The second identity says something similar.2012-02-11
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    @André: Could you explain that a bit please? How do these pairs of divisors occur? And did you really mean $ab=1$? Modulo something?2012-02-20
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    @Lando: If you don't already know them, you might be interested in the [Jacobi triple product](http://en.wikipedia.org/wiki/Jacobi_triple_product) and the [pentagonal number theorem](http://en.wikipedia.org/wiki/Pentagonal_number_theorem).2012-02-20
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    (Like Euler pentagonal theorem, this identity follows from Jacobi triple product.)2013-12-01
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    @GrigoryM Do you know where I can see it derived from the Jacobi triple product?2016-02-21

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