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Fourier Series Proof

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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.

See Also This Related BrainMass Solution

Use Parseval's equality

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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