Consider the function f(r): = cos ar on the interval [-,] when a is not an...
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Consider the function f(r): = cos ar on the interval [-,] when a is not an integer. (a) Show that (-1)"+1 n2 - a? 2a sin an COS (Lr = COS nr 2a2 n=1 for -T <r<T. (b) What happens when a is not an integer? (c) Use the Weierstrauss M-Test to prove that the Fourier series of cos ar converges uniformly for -<r < T. Consider the function f(r): = cos ar on the interval [-,] when a is not an integer. (a) Show that (-1)"+1 n2 - a? 2a sin an COS (Lr = COS nr 2a2 n=1 for -T <r<T. (b) What happens when a is not an integer? (c) Use the Weierstrauss M-Test to prove that the Fourier series of cos ar converges uniformly for -<r < T.
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