Results 1 to 4 of 4

Math Help - Analysis

  1. #1
    Junior Member
    Joined
    Oct 2008
    Posts
    38

    Analysis

    I have been asked to give an example of a sequence in C (complex) which tends to zero but the principal value if the argument does not tend to a limit.

    I know that one example would be Zn=(-1)*n/n for n>=1.

    However i don't understand how the principal value alternates between pi and 0 for this example, or how to calculate the principal value for a complex sequence in general.

    Any help wold be greatly appreciated. Thanks.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,916
    Thanks
    1762
    Awards
    1
    If you mean z_n  = \frac{{\left( { - 1} \right)^n }}{n}, then yes that works,
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Oct 2008
    Posts
    38
    Can you please explain how to calculate the principal value of the argument of this example.

    Also, how do i find other examples?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,916
    Thanks
    1762
    Awards
    1
    Arg\left( {z_n } \right) = \left\{ {\begin{array}{rl}<br />
   0, & {\mbox{n is even}}  \\<br />
   \pi ,  & {\mbox{n is odd}}  \\ \end{array} } \right.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Help with Analysis please :)
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: October 16th 2009, 05:38 AM
  2. analysis help
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: October 8th 2009, 04:11 PM
  3. analysis help
    Posted in the Calculus Forum
    Replies: 0
    Last Post: January 19th 2009, 03:38 PM
  4. analysis
    Posted in the Calculus Forum
    Replies: 2
    Last Post: December 15th 2008, 04:07 PM
  5. Analysis Help
    Posted in the Calculus Forum
    Replies: 1
    Last Post: September 8th 2008, 06:59 PM

Search Tags


/mathhelpforum @mathhelpforum