order of factors in infinite product

Theorem.

If the infinite product

$$\prod _{\nu =1}^{\mathrm{\infty }}(1+c_{\nu })=(1+c_1)(1+c_2)\mathrm{\cdots }$$

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

Title	order of factors in infinite product
Canonical name	OrderOfFactorsInInfiniteProduct
Date of creation	2013-03-22 14:37:27
Last modified on	2013-03-22 14:37:27
Owner	pahio (2872)
Last modified by	pahio (2872)
Numerical id	11
Author	pahio (2872)
Entry type	Theorem
Classification	msc 30E20
Related topic	AbsoluteConvergenceOfInfiniteProductAndSeries
Related topic	ConvergenceOfComplexTermSeries
Related topic	SumOfSeriesDependsOnOrder
Defines	value of an infinite product