Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

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,

share|improve this question
    
$f(0)$ is 0, independently of $q$ (as long as $q\neq 0$). –  Alex B. Jul 15 '11 at 7:16
    
Actually I meant n=1. Sorry for the confusion. –  Ufo Jul 15 '11 at 7:26
2  
I would suggest asking this at math.stackexchange.com –  Gjergji Zaimi Jul 15 '11 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 '11 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 '11 at 8:25

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.