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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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    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: a rather fascinating subject I'll admit...2012-12-13