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Math Help - Complex fourier series

  1. #1
    Member roshanhero's Avatar
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    Complex fourier series

    While deriving complex fourier series I have reached at c_0+\sum_{n=1}^{n=\infty}c_ne^{\frac{in\pi x}{l}}+\sum_{n=-1}^{n=-\infty}c_ne^\frac{in\pi x}{l}.
    Can anyone tell me what combined expression (pattern) can be written for this and why?
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  2. #2
    MHF Contributor
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    You notice that when n = 0 then c_n e^{\frac{i n \pi x}{L}}= c_0 so your entire sum can be written as

    so  \sum \limits_{n = -\infty}^{-1} c_n e^{\frac{i n \pi x}{L}} + c_0 + \sum \limits_{n = 1}^{\infty} c_n e^{\frac{i n \pi x}{L}} = \sum \limits_{n = -\infty}^{\infty} c_n e^{\frac{i n \pi x}{L}}
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