Hello:

I have this function:

whose domain is the line:

I need to find the analytic continuation for the whole complex plane. I don't know how to start it.

Thank you!

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- May 13th 2010, 06:21 PMBop[SOLVED] find analytic continuation
Hello:

I have this function:

whose domain is the line:

I need to find the analytic continuation for the whole complex plane. I don't know how to start it.

Thank you! - May 14th 2010, 01:05 AMOpalg
- May 14th 2010, 07:57 AMBop
Hello, thanks for answering, here what i've done:

as

so

we know

so

This is what you meant? If it is, I don't understand why we have to do this to obtain the analytic continuation for the whole complex plane.

Thank you! - May 14th 2010, 08:33 AMOpalg
Yes, that is what I meant (apart from the mistake at the end). The reason for doing it that way is that if you want f to be an analytic function of z then you have to express it in terms of z. Fortunately, you end up with the expression , which certainly is analytic on the whole complex plane, and therefore gives the required analytic continuation for f(z).