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Regarding Fourier series

  1. Dec 26, 2013 #1
    1. The problem statement, all variables and given/known data
    This is a general question, no real problem statement and is connected to solving Fourier series. You know that to solve it, you need to find [itex]a_{n}[/itex], [itex]a_{0}[/itex] and [itex]b_{n}[/itex].

    2. Relevant equations
    When solving the above mentioned ''coefficients'' you can get a solution with [itex]sin[/itex] or [itex]cos[/itex] which, in the case of [itex]cos(n\pi)[/itex] can be written as [itex](-1)^{n}[/itex] where [itex]n=0,1,2,...[/itex] since the solution alternates between [itex]0,1,-1[/itex]. Is there any similar way to write (or solve) [itex]sin[/itex] or [itex]cos\frac{n\pi}{2}[/itex] since the solution follows this pattern [itex]1,0,-1,0,1,0,-1,...[/itex]

    Thank you in advance!
     
  2. jcsd
  3. Dec 26, 2013 #2

    vela

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    Typically you then have only odd or even terms, e.g. ##a_k \cos (k\omega t), k=1, 3, 5,\dots##. You can reindex the series using the substitution k=2n+1 or k=2n. The alternating sign is conveniently expressed by (-1)n or (-1)n+1.
     
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