Results 1 to 3 of 3

Math Help - Prove that F'(z) = f(z) by Power Series expansion.

  1. #1
    Member
    Joined
    Oct 2009
    Posts
    195

    Prove that F'(z) = f(z) by Power Series expansion.



    Please focus on 19-b) at the bottom. I'm not sure how hard this is supposed to be, or where |z-z_0| < R comes in. I think I must be missing something.

    Thanks!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Drexel28's Avatar
    Joined
    Nov 2009
    From
    Berkeley, California
    Posts
    4,563
    Thanks
    21
    Quote Originally Posted by davismj View Post


    Please focus on 19-b) at the bottom. I'm not sure how hard this is supposed to be, or where |z-z_0| < R comes in. I think I must be missing something.

    Thanks!
    You need the fact that |z-z_0|< R to ensure that your move of the derivative from outside the sum to inside was kosher.
    Last edited by Jhevon; February 21st 2010 at 10:33 PM. Reason: fixed LaTeX
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Oct 2009
    Posts
    195
    Quote Originally Posted by Drexel28 View Post
    You need the fact that |z-z_0|< R to ensure that your move of the derivative from outside the sum to inside was kosher.
    Can you explain (or give an example or something) of why it wouldn't work if |z-z_0| > R?

    Actually, nevermind. I'm being lazy, I know this one.

    As always, Thanks!

    Also, are you really an undergraduate freshman?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. power series expansion
    Posted in the Calculus Forum
    Replies: 6
    Last Post: January 16th 2010, 01:56 PM
  2. power series expansion II
    Posted in the Calculus Forum
    Replies: 3
    Last Post: January 12th 2010, 04:42 AM
  3. Power series expansion
    Posted in the Calculus Forum
    Replies: 1
    Last Post: January 2nd 2010, 09:15 AM
  4. Power series expansion!!
    Posted in the Calculus Forum
    Replies: 1
    Last Post: February 5th 2009, 10:14 PM
  5. Power Series Expansion
    Posted in the Calculus Forum
    Replies: 1
    Last Post: February 2nd 2009, 04:44 PM

Search Tags


/mathhelpforum @mathhelpforum