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Difficult question from some test somewhere (I forget).

$$\prod_{x=2}^\infty\frac{x^4-1}{x^4+1}$$

$x$ is, of course, an integer.

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    There are some [relevant closed forms here](http://mathworld.wolfram.com/InfiniteProduct.html) but it still isn't helping me understand the solution. :(2012-12-11
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    When $x=1$, $x^4-1 = 0$. So, the whole product is zero. Are you sure there isn't a typo??2012-12-11
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    The OP likely means for the bottom index to be $2$, especially since the closed form in the link provided above also defines the bottom index to be $2$.2012-12-11
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    @dexter04 The bottom index is in fact $2$. Whoops. Bad typo.2012-12-11
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    Isn't this just (11) at that link? And doesn't it give a reference to a publication of Borwein?2012-12-11
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    @GerryMyerson There's no proof, though; only a citation and result. Also, guessing by the cited book, Borwein's proof is heavily computational and cannot be done with pen and paper.2012-12-11
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    You can't tell a book by its cover. If you want the answer, you know where to look. If, after you've looked, you're not satisfied, come to report back on what you've found. Meantime, I'm not going to worry about something that might have been on some unreferenced test somewhere sometime.2012-12-11
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    @GerryMyerson I guess I'm a little unwilling to pay money to solve one problem. Also, on the directly referenced pages, Borwein just lists Maple's results for these computations. I imagine he explains them a few pages later, but that's not free to preview.2012-12-11
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    You can try proving the result by working backwards. There are mentions in the link above of the closed form as a product of gamma functions. Perhaps if you look at the Weierstrass factorization of the gamma function you can plug in the right values to get your original product.2012-12-11
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    Do you not have access to a library, 1. e4 c6 ?2012-12-11
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    @Gerry: Perhaps an open(ing) library? ;-)2012-12-12
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    @joriki, good one.2012-12-12

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