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Have come across the following infinite product:

$\prod_{n=1}^{inf} (1+ax^n)$

where for practicality 0<x<1 and 0<a<1

After much searching through old calculus notes and 2 straight days of google searching I still can't tell if this infinite product has a closed form. I'm not asking for the actual closed form, just wandering if one actually exists? And if one does exist, a nudge in the right direction would be appreciated. One of the websites I visited showed something kind of similar based on q-analoges from combinatorial theory, however this didn't really seem like what I was after.

thanks, q :)

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# Closed form of infinite product

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