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# 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, then its value, i.e. $\displaystyle\lim_{{n\to\infty}}\prod_{{\nu=1}}^{n}(1\!+\!c_{\nu})$, does not depend on the order of its factors and vanishes only when some factor is zero.

Defines:

value of an infinite product

Related:

AbsoluteConvergenceOfInfiniteProductAndSeries, ConvergenceOfComplexTermSeries, SumOfSeriesDependsOnOrder

Type of Math Object:

Theorem

Major Section:

Reference

Groups audience:

## Mathematics Subject Classification

30E20*no label found*

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