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Possible Duplicate:
Limit of a particular variety of infinite product/series

Define $$F(x) = \prod_{n=1}^\infty(1-x^n)$$ where $|x|<1$.

How can one compute $F(1/2)$? (Without an obvious polynomial expansion or brute-force calculation.)

This is sometimes called Euler's function.

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    Some related [information](http://math.stackexchange.com/questions/3776/limit-of-a-particular-variety-of-infinite-product-series) (no 'closed form').2012-12-13
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    Quick simulation stops around 0.288788...2012-12-13
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    @RaymondManzoni that's a great source. Nearly as good as a closed form.2012-12-13
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    Glad it helped @AlecS but I fear we will have to close this as duplicate!2012-12-13

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That product is not so simple as you think. Euler proved that $$F(x) = \prod_{n=1}^\infty(1-x^n)=\sum_{-\infty}^{+\infty}(-1)^kx^{\frac{k(3k+1)}{2}}$$ This problem arises in partition number theory and is called Euler's pentagonal number theorem.

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    @AlecS: This [paper](http://arxiv.org/abs/math/0510054v2) from Bell may help you too.2012-12-13
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    @RaymondManzoni I had begun reading it already. :)2012-12-13
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    @AlecS: a rather fascinating subject I'll admit...2012-12-13