# 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 |