Something nice that came across with:

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

Printable View

- Aug 17th 2011, 10:18 PMAlso sprach ZarathustraInfinite Product.
Something nice that came across with:

Is the product $\displaystyle \prod_{n=0}^{\infty}\frac{\beta +n}{\alpha+n }$ converge or diverge? - Aug 17th 2011, 10:45 PMCaptainBlackRe: Infinite Product.
Nice. Obvious when $\displaystyle \alpha=\beta$, when these are not equal taking logs and considering the convergence of the resulting series seems to work a treat.

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

CB - Aug 17th 2011, 11:10 PMAlso sprach ZarathustraRe: Infinite Product.