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
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
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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