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Fourier series of abs(sin(x))

160
3
1. The problem statement, all variables and given/known data
Hello,

i am trying to do find the Fourier series of abs(sin(x)), but have some problems. As the function is even, bn = 0. I have calculated a0, and I am now working on calculating an. However, when looking at the solution manual, they have set up one calculation for n > 1 (i.e. a2, a3, a4, a5... and so on) and one for n = 1 (i.e. a1). Why?

2. Relevant equations


3. The attempt at a solution
 

stevendaryl

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Well, you need to compute ##\int cos(nx) sin(x) dx##. You can use a trig identity to rewrite that in terms of ##sin((n+1) x)## and ##sin((n-1)x)##. The case ##n=1## is special, because the second term is zero.
 
160
3
Thank you!!
 

Ray Vickson

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1. The problem statement, all variables and given/known data
Hello,

i am trying to do find the Fourier series of abs(sin(x)), but have some problems. As the function is even, bn = 0. I have calculated a0, and I am now working on calculating an. However, when looking at the solution manual, they have set up one calculation for n > 1 (i.e. a2, a3, a4, a5... and so on) and one for n = 1 (i.e. a1). Why?

2. Relevant equations


3. The attempt at a solution
What interval are you using? ##[-\pi,\pi]?## ##[0, \pi]?## ##[0, 2\pi]?##
 

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