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Math Help - fourier series if period is π... help

  1. #1
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    fourier series if period is π... help

    Q2 )Expand f(x) = sin x, -π/2 <x <π/2, in a Fourier series if the period is π.

    hope got ppl can help me, thx~~~~~ T_T_T_T_T_T_T
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  2. #2
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    Quote Originally Posted by helpless View Post
    Q2 )Expand f(x) = sin x, -π/2 <x <π/2, in a Fourier series if the period is π.

    hope got ppl can help me, thx~~~~~ T_T_T_T_T_T_T
    Just like the other one:

    The Fourier Series periodic with period 2L, L>0 is defined to be:

    (a_0)/2 + sum_{n=1 to infty} [a_n cos(n pi x/L) + b_n sin(n pi x/L)]

    where:

    a_n = (1/L) integral_{x=-L to L} f(x) cos(n pi x/L) dx

    b_n = (1/L) integral_{x=-L to L} f(x) sin(n pi x/L) dx

    Now consider f(x) periodic with period pi, where:

    f(x) = sin(x), -pi/2<x<pi/2


    Now f(x) is odd so all the integrals for the "a" terms are zero. So lets now
    consider the "b" terms, here L=pi/2 so:

    b_n = (2/pi) integral_{x=-pi/2 to pi/2} sin(x) sin(2 n x) dx

    Which I hope I can leave to you.

    RonL
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