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June 6th, 2011, 02:53 AM   #1
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Taylor series about i

Can anybode help me with the following question:

Use Taylorís 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
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June 6th, 2011, 03:29 PM   #2
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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.
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June 7th, 2011, 03:24 AM   #3
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Re: Taylor series about i

So we could say: |z+i| < 1

This is correct?

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June 7th, 2011, 03:35 PM   #4
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Re: Taylor series about i

No. |z-i| < 1.
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