Infinite Product.

**Also sprach Zarathustra** · August 17th 2011, 10:18 PM

Something nice that came across with:

Is the product $\prod_{n=0}^{\infty}\frac{\beta +n}{\alpha+n }$ converge or diverge?

**CaptainBlack** · August 17th 2011, 10:45 PM

Originally Posted by Also sprach Zarathustra

Something nice that came across with:

Is the product $\prod_{n=0}^{\infty}\frac{\beta +n}{\alpha+n }$ converge or diverge?

Nice. Obvious when $\alpha=\beta$ , when these are not equal taking logs and considering the convergence of the resulting series seems to work a treat.

(If $\alpha$ and/or $\beta$ are/is negative a bit more care is needed but it still seems to work)

CB

**Also sprach Zarathustra** · August 17th 2011, 11:10 PM

Originally Posted by CaptainBlack

Nice. Obvious when $\alpha=\beta$ , when these are not equal taking logs and considering the convergence of the resulting series seems to work a treat.

CB

Yes!

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