Find the orthogonal expansion (generalized Fourier series) for f ( x ) = { 0 , − 1 < x < 0 1 , 0 < x < 1 in terms of the orthonormal system of Problem 26 26. Show that the set of functions { cos π 2 x , sin π 2 x , cos 3 π 2 x , sin 3 π 2 x , ⋯ , cos ( 2 n − 1 ) π 2 x , sin ( 2 n − 1 ) π 2 x , ... } is an orthonormal system on [ − 1 , 1 ] with respect to the weight function w ( x ) = 1 .
Find the orthogonal expansion (generalized Fourier series) for f ( x ) = { 0 , − 1 < x < 0 1 , 0 < x < 1 in terms of the orthonormal system of Problem 26 26. Show that the set of functions { cos π 2 x , sin π 2 x , cos 3 π 2 x , sin 3 π 2 x , ⋯ , cos ( 2 n − 1 ) π 2 x , sin ( 2 n − 1 ) π 2 x , ... } is an orthonormal system on [ − 1 , 1 ] with respect to the weight function w ( x ) = 1 .
Using and Understanding Mathematics: A Quantitative Reasoning Approach (6th Edition)
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