Assuming thatf(x) = a02 +n=1an cos nxL + bn sin nxL,
Chapter 10, Problem 17(choose chapter or problem)
Assuming thatf(x) = a02 +n=1an cos nxL + bn sin nxL, (i)show formally that1LLL[f(x)]2 dx = a202 +n=1(a2n + b2n).This relation between a function f and its Fourier coefficients is known as Parsevals6equation. This relation is very important in the theory of Fourier series; see inSection 11.6.Hint:Multiply Eq. (i) by f(x),integrate from L to L, and use the EulerFourier formulas.
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