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Fourier Series

  1. Dec 10, 2013 #1
    Simple question;


    gGj1NsO.jpg

    Why isn't it [itex]\sum[/itex] am (from m=1 to infinity)

    Thanks in advance.
     
    Last edited: Dec 10, 2013
  2. jcsd
  3. Dec 10, 2013 #2

    jbunniii

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    In the first line, ##f(x)## was replaced with its Fourier series expansion:
    $$f(x) = a_0 + \sum_{n=1}^{\infty}(a_n \cos nx + b_n \sin nx)$$
    The ##n## is the index over which the sum is taken. The name of this index is arbitrary. In principle you could use ##m## instead:
    $$f(x) = a_0 + \sum_{m=1}^{\infty}(a_m \cos mx + b_m \sin mx)$$
    However, in this case that would cause a conflict because ##m## is already in use in the integrand on the left hand side:
    $$\int_{-\pi}^{\pi} f(x) \cos mx dx$$
     
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