# 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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https://brainmass.com/math/fourier-analysis/use-parsevals-equality-60430

#### Solution Preview

Please see the attachment.

12.5-2

Proof:

First, we find the Fourier series of the function ,

The Fourier series of ...

#### Solution Summary

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