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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: 6,641 Thanks: 625  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: 6,641 Thanks: 625  Re: Taylor series about i
No. zi < 1.


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