# Fourier Series Proof

Please see the attached file for full problem description.

Q = e^ (i n pi alpha) + e^ (-i n pi alpha)

and Q = 0. How can Q be two different things?

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#### Solution Summary

The proof is centered on the relations Q = e^ (i n pi alpha) + e^ (-i n pi alpha) and Q =0. The solution is well explained.

Use Parseval's equality

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

(See attached file for full problem description)

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12.5-2

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 .

If

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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