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2. Use the Fourier series of to prove the identities and Σ n=1 f(x)=x₁ == // < x < 1/1 (-1)"+1 2n-1 = 1 1 1 1 = 1+ + 22 32 1 5 || RIT || π 226 Hint: Let x = for the first identity and for the second use Plancherels iden- tity with the Fourier series expressed in terms of the basic vectors {√2sin (2πnx)

2. Use the Fourier series of to prove the identities and Σ n=1 f(x)=x₁ == // < x < 1/1 (-1)"+1 2n-1 = 1 1 1 1 = 1+ + 22 32 1 5 || RIT || π 226 Hint: Let x = for the first identity and for the second use Plancherels iden- tity with the Fourier series expressed in terms of the basic vectors {√2sin (2πnx)

Advanced Engineering Mathematics
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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homework practice, this class is about Fourier series; generalized functions; and numerical methods.

please show clear, thanks.

2. Use the Fourier series of to prove the identities and ∞ Σ n=1 f(x)=x₂ (−1)n+1 2n - 1 =<x</ 1 Σ 1+ + n² 3 + 22 32 1 5 || BIT π Hint: Let x = for the first identity and for the second use Plancherels iden- tity with the Fourier series expressed in terms of the basic vectors {√2sin (2лnx)}.
Transcribed Image Text:2. Use the Fourier series of to prove the identities and ∞ Σ n=1 f(x)=x₂ (−1)n+1 2n - 1 =<x</ 1 Σ 1+ + n² 3 + 22 32 1 5 || BIT π Hint: Let x = for the first identity and for the second use Plancherels iden- tity with the Fourier series expressed in terms of the basic vectors {√2sin (2лnx)}.
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