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#1 2009-04-26 00:03:51

coffeeking
Member
Registered: 2007-11-18
Posts: 44

complex function

Hi, please check if I have made any mistake.

Determine if

contain a primitive on
.

Below is my working:


has primitive
where

Since

has analytic domain

where

Therefore,

does not has a primitive on
.

Thanks in advance.

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#2 2009-04-26 01:29:09

dannyv
Member
Registered: 2007-09-20
Posts: 34

Re: complex function

Hi, it seems correct, the only obscure part for me was the following:

coffeeking wrote:

Since

has analytic domain

But after looking at it for a couple of minutes it became clear. If you write the complex logarithm it is easier.

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#3 2009-04-26 01:57:25

coffeeking
Member
Registered: 2007-11-18
Posts: 44

Re: complex function

Hi dannyv, thanks for the effort smile

By the way could you elaborate what do you mean by if I write the complex logarithm it is easier?

Thanks.

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#4 2009-04-26 02:36:27

Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791

Re: complex function

coffeeking, as long as you are familiar with branch cuts, I'd say you don't need to show any more work than that.

But remember that log(z-1) has many analytic domains, depending on how you take your argument to be.  It is true though that every single one of these domains does not include C \ {1}.


"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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#5 2009-04-26 03:01:16

coffeeking
Member
Registered: 2007-11-18
Posts: 44

Re: complex function

Hi Ricky thanks for the info up

I have to say that there are lots of helpful helper here thanks! big_smile

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