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 June 6th, 2011, 03:53 AM #1 Newbie   Joined: Feb 2011 Posts: 24 Thanks: 0 Taylor series about i Can anybode help me with the following question: Use Taylor’s Theorem to determine the Taylor series about i for the function f(z)= z +Logz , giving an expression for the general term of the series. Also, state the largest open disc on which the function f is represented by this Taylor series. Until now I tried all derivatives, but I cannot get a general term and cannot find the largest open disc. I know that the function is analytic on the region C without x<= 0. Please help
 June 6th, 2011, 04:29 PM #2 Global Moderator   Joined: May 2007 Posts: 6,683 Thanks: 658 Re: Taylor series about i The singularity for logz is at z=0, so the largest open disc is the disc centered at z=i and radius 1.
 June 7th, 2011, 04:24 AM #3 Newbie   Joined: Feb 2011 Posts: 24 Thanks: 0 Re: Taylor series about i So we could say: |z+i| < 1 This is correct? Math
 June 7th, 2011, 04:35 PM #4 Global Moderator   Joined: May 2007 Posts: 6,683 Thanks: 658 Re: Taylor series about i No. |z-i| < 1.

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