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Use Parseval's equality

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We are using the book Methods of Real Analysis by Richard R. Goldberg

(See attached file for full problem description)

Show that the Fourier series for is

a) Use 12.5E to show that Fourier series at t=0 converges to . Deduce that

12.5E: Theorem. Let ( this means the function f and the function g is Lebesgue Integrable on , we can write , page 318 of the book Methods if real
analysis by Richard R. Goldberg), and let x be any point in .
and exist, then the Fourier series for at x will converge to .

b) Use Parseval's equality to show that

Parseval's equality:

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First, we find the Fourier series of the function ,
The Fourier series of ...

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This solution is comprised of a detailed explanation to use Parseval's equality to solve.