# order of factors in infinite product

###### Theorem.

If the infinite product

 $\prod_{\nu=1}^{\infty}(1\!+\!c_{\nu})=(1\!+\!c_{1})(1\!+\!c_{2})\cdots$

of complex numbers $1\!+\!c_{\nu}$ is absolutely convergent (http://planetmath.org/AbsoluteConvergenceOfInfiniteProduct), then its value, i.e.  $\displaystyle\lim_{n\to\infty}\prod_{\nu=1}^{n}(1\!+\!c_{\nu})$, does not depend on the is zero.

Title order of factors in infinite product OrderOfFactorsInInfiniteProduct 2013-03-22 14:37:27 2013-03-22 14:37:27 pahio (2872) pahio (2872) 11 pahio (2872) Theorem msc 30E20 AbsoluteConvergenceOfInfiniteProductAndSeries ConvergenceOfComplexTermSeries SumOfSeriesDependsOnOrder value of an infinite product