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Math Help - Fourier Cosine series of cos(x)

  1. #1
    Junior Member
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    Fourier Cosine series of cos(x)

    Hello peoples,

    I think this is a trick question... well sort of :P



    for part (a) i get that the cosine Fourier Series for f(x) = cos(x) to be:



    i hope that is ok, but its part (b) that is troubling me...

    is all that happens as is that the cosine Fourier series of cos(x) goes to 0?

    i am guessing i am missing some trick to this question?

    Cheers!

    Sarah
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by sarahisme View Post
    Hello peoples,

    I think this is a trick question... well sort of :P



    for part (a) i get that the cosine Fourier Series for f(x) = cos(x) to be:



    i hope that is ok, but its part (b) that is troubling me...

    is all that happens as is that the cosine Fourier series of cos(x) goes to 0?

    i am guessing i am missing some trick to this question?

    Cheers!

    Sarah
    Look at the limit of the coefficient of cos(pi x /alpha) as alpha goes to
    pi.

    You should find that the limit as alpha goes to pi of all the coeficients
    other than that of cos(pi x /alpha) are 0, while that of cos(pi x /alpha)
    is 1.

    RonL
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  3. #3
    Junior Member
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    Quote Originally Posted by CaptainBlack View Post
    Look at the limit of the coefficient of cos(pi x /alpha) as alpha goes to
    pi.

    You should find that the limit as alpha goes to pi of all the coeficients
    other than that of cos(pi x /alpha) are 0, while that of cos(pi x /alpha)
    is 1.

    RonL
    i yep i see, i need to be more careful with the n = 1 term when alpha = pi.

    thanks for the help!
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