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Fourier coefficients - dirichlet problem for annulus

  • Thread starter Dassinia
  • Start date
  • #1
144
0
Hello

1. Homework Statement

Find the Fourrier coefficients in the annulus problem of the text.
uxx+uyy=0 in 0<a²<x²+y²<b²
u=g(θ) for x²+y²=a²
u=h(θ) for x²+y²=b²

Homework Equations


The solution is
upload_2016-4-21_17-42-38.png


The Attempt at a Solution


I have the solutions but when I solved it for Co and Do I didn't get the same thing, but or all the other coefficients I got the right thing.

Here is the problem
To get Co and Do I did the integral on both sides from 0 to 2π to get rid of the sum.
So I ended up with
upload_2016-4-21_17-47-2.png


But the solution give a factor 1/π Before the integral of h and g , why ?
Thank you !
 

Answers and Replies

  • #2
18,086
7,507
Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
 
  • #3
1,845
88
Try $$\int_0^{2\pi}u(a,\theta) \, d \theta$$ and see what you get. You'll have two sides, one is ##g## and the other is the long series you've posted.
 

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