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Fourier Series in cylindrical coordinate

  1. May 25, 2016 #1
    1. The problem statement, all variables and given/known data
    Here is my question
    1380578000_1464176740.png

    2. Relevant equations
    I don't know with what formula does the book find fourier series?

    3. The attempt at a solution
     
  2. jcsd
  3. May 26, 2016 #2
    Have you tried writing an expression for the current?
     
  4. May 27, 2016 #3
    Hello deskswirl
    Yes , But I know the fourier series for 2-dimensional in cartesian coordinate not cylindrical fourier series.I can do and follow the math procedures.I want to know the main formula that I can derive above equation.
     
  5. May 29, 2016 #4
    One of the most general forms for the Fourier-Bessel series is given by:
    $$\sum\limits_{q}{\sum\limits_{p}{\left\{ \begin{matrix} {{J}_{p}}\left( qr \right) \\ {{Y}_{p}}\left( qr \right)\\\end{matrix} \right\}\left\{ \begin{matrix}
    \sin \left( p\phi \right) \\ \cos (p\phi ) \\\end{matrix} \right\}\left\{ \begin{matrix} {{e}^{qz}} \\ {{e}^{-qz}} \\\end{matrix} \right\}}}$$
    Another is found by letting $$q\to iq$$ in the above expression. These are the two primary solutions of Laplace's equation in circular-cylinder coordinates. Typically due to the symmetry of the problem in phi or z the expression becomes simpler.
     
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