Math 415 Quiz 7B Find the Fourier series for f ( x ) =-x,-π ≤ x < π ; f ( x + 2) = f ( x ) . What function does it actually converge to? As the function is odd, we know that a k = 0 for k = 0, 1, 2, . . . So we just have to calculate b k : b k = 1 π Z π-π-x sin kxdx =-2 π Z π0 x sin kxdx = 2(-1) k k . And so the Fourier series for f is ∞ X k =1 2(-1) k k sin kx. By the Fourier convergence theorem it converges to ˜ f = -x if-π < x < π0 for
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This note was uploaded on 07/26/2011 for the course MATH 415 taught by Professor Costin during the Spring '07 term at Ohio State.