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I Q about Fourier Coefficient Derivation

  1. Mar 30, 2016 #1
    For the calculation of cn u have to multiply the equation

    ∑ cn * ejnx

    what is the reason for this? in my textbook it says nothing about it and on some sites it just said "without justification"
    i guess what im asking is why does this do what we want?
    ps: how do u properly make equations here?
  2. jcsd
  3. Mar 30, 2016 #2


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    Science Advisor
    Homework Helper

    It's not just multiplication, but you also have to integrate the resulting product function. It's done this way because
    \int_{0}^L \exp\left(\frac{2\pi}{L}(m-n)u\right) du \propto \delta_{mn}
  4. Mar 30, 2016 #3


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    Gold Member

    Yes, the elements ##\{e^{jnx}\}## form an orthonormal system on your Hilbert space ...
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