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Topic: Help with identity
Replies: 15   Last Post: May 9, 2013 7:13 AM

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Mike Trainor

Posts: 28
Registered: 4/21/13
Re: Help with identity
Posted: May 2, 2013 7:07 PM
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On Thu, 02 May 2013 09:41:43 +0100, Robin Chapman
<R.J.Chapman@ex.ac.uk> wrote:



>> But, I have a question. What above the
>> z^n term in the numberator that comes due
>> to the numerator that should be there from
>> the cos(ny) part? That messes up things as
>> the residues now have exp(-n*x) and,
>> unforturnately, exp(n*x). Other than that,
>> it all works out.

>
>No we don't. Put z = cos(y) + i sin(y) = exp(iy).
>What is z^n in terms of y?


Finally dug out the books and saw an example
of how to do these integrals -- suddenly
everything came back. The book had a example
of how to do the integral of

cos(3*x)/(a - cos(x))

They did have z^3 + z^(-3) in the denominator
and messed with the 3rd order pole. But, in the
margin, in my own hand was a note saying that
z^3 is enough and that the residues add up to
the same either way!!

Irony (and atrophy), I guess.

Thanks again.

mt



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