6. Assume that the Fourier series of a function (x) on [-L, L] converges to f(x). (a) Derive the Parseval's equation + Σ(a² + b²) = ± √ P(x) dx, where 30., and b, are Fourier coefficients. (b) Use Parseval's equation to show that when /(x) = x for -π ≤x≤n. n-1

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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6. Assume that the Fourier series of a function (x) on [-L, L] converges to
(x).
(a) Derive the Parseval's equation
E(a; + bi) = + | f(x)dx, where ao,a, and b, are Fourier coefficients.
2
L
(b) Use Parseval's equation to show that
* when (x) = x for
Transcribed Image Text:6. Assume that the Fourier series of a function (x) on [-L, L] converges to (x). (a) Derive the Parseval's equation E(a; + bi) = + | f(x)dx, where ao,a, and b, are Fourier coefficients. 2 L (b) Use Parseval's equation to show that * when (x) = x for
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