Assuming that f(x) = a0 2 + n=1 an cos nx L + bn sin nx L , (i) show formally that 1 L L
Chapter 10, Problem 17(choose chapter or problem)
Assuming that f(x) = a0 2 + n=1 an cos nx L + bn sin nx L , (i) show formally that 1 L L L [f(x)] 2 dx = a2 0 2 + n=1 (a2 n + b2 n). This relation between a function f and its Fourier coefficients is known as Parsevals6 equation. This relation is very important in the theory of Fourier series; see in Section 11.6. Hint: Multiply Eq. (i) by f(x),integrate from L to L, and use the EulerFourier formulas.
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