(Fourier series) Show that the constants ak, .k D 0; 1; 2; :
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(Fourier series) Show that the constants ak, .k D 0; 1; 2; : : : ; n/, and bk, .k D 1; 2; : : : ; n/, which minimize the
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(Fourier series) Show that the constants ak, .k D 0; 1; 2; : : : ; n/, and bk, .k D 1; 2; : : : ; n/, which minimize the integral In D Z ? " f .x/ ? a0 2 ? Xn kD0 ak cos kx C bk sin kx #2 dx; are given by ak D 1 Z f .x/ cos kx dx; bk D 1 Z f .x/sin kx dx: Note that these numbers, called the Fourier coefficients of f on
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