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## Homework Statement

For a given periodic function F(x), the coefficients A

_{n}of its Fourier expansion can be found using the formulas (Form1) and (Form2). Consider a periodic square pulse and verify that the Fourier coefficients are as claimed:

A

_{n}=([itex]\frac{2}{πn}[/itex])sin([itex]\frac{πan}{λ}[/itex])

for n≥1 and that

A

_{0}= [itex]\frac{a}{λ}[/itex]

(the height of the pulse is 1, the width is a)

## Homework Equations

(Form1): A

_{n}= [itex]\frac{1}{λ}[/itex][itex]\int^{λ}_{0}[/itex] F(x)cos([itex]\frac{2πnx}{λ}[/itex]) dx

(Form2): A

_{0}= [itex]\frac{1}{λ}[/itex][itex]\int^{λ}_{0}[/itex] F(x)dx

λ = wavelength

F(x) = A

_{n}cos([itex]\frac{2πnx}{λ}[/itex])

## The Attempt at a Solution

I've tried to integrate the function F(x) through Form1, but my answer doesn't match the one that it should be. I'm missing a [itex]\frac{1}{πn}[/itex] and my sine value has a 4 in it. Then I tried without the extra cos(~) part in Form1, where ~ is the fraction within the cos (I don't want to rewrite it over and over). I was closer this time, but I couldn't get a λ in the denominator of the fraction within the sine value.

I know these attempts would be better seen had I actually written them out, but I assure you I've tried to integrate according to the functions I'm given to no avail. The textbook doesn't do a good job explaining how to calculate the Fourier coefficients as it just handwaves it under the guise of it being "straightforward". I would appreciate someone pointing me in the right direction, or someone showing what I need to start with to solve this problem as I suspect the given Formulas (Form1 and Form2) only apply to their respective question (they were part of another question, but the question I'm on directed me to them as the formulas to use).

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