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Fourier coefficients - dirichlet problem for annulus

  1. Apr 21, 2016 #1

    1. The problem statement, all variables and given/known data

    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

    2. Relevant equations
    The solution is

    3. 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

    But the solution give a factor 1/π Before the integral of h and g , why ?
    Thank you !
  2. jcsd
  3. Apr 26, 2016 #2
    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?
  4. Apr 27, 2016 #3


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    Gold Member

    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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