Infinite Product

Hi there,

It has been long time since I had my math classes. However, I am trying to find a close form expression (if exists) of the following infinite product

$f(n) =\prod\limits_{i=n}^{\infty} (1-\frac{1}{q^i})$.

I am looking for an expression or approximation that represents the product. In particular, the case when q=2 and n=1 is of interest. But, the general equation is also important to me.

If you can refresh my memory on where I would find the needed material to do the above, or help with some clues, I would be really grateful.

Thanks,

edited Jul 15 2011 at 7:27

asked Jul 15 2011 at 7:11

Ufo
1●1

$f(0)$ is 0, independently of $q$ (as long as $q\neq 0$). – Alex Bartel Jul 15 2011 at 7:16

Actually I meant n=1. Sorry for the confusion. – Ufo Jul 15 2011 at 7:26

I would suggest asking this at math.stackexchange.com – Gjergji Zaimi Jul 15 2011 at 7:35

For $n=1$ it's q-Pochhammer symbol $(q^{-1},q^{-1})_\infty$ en.wikipedia.org/wiki/Q-Pochhammer_symbol – Andrew Jul 15 2011 at 7:38

For n=1 the series expansion is Euler's pentagonal number theorem. See e.g. en.wikipedia.org/wiki/Pentagonal_number_theorem. – Johann Cigler Jul 15 2011 at 8:25

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