Question

find the fourier sine series of the function F(x) = 2x in (0,1)

​

Answer 1

Answer:

I was given the problem to find the Fourier Sine Series for f(x)=1+x on the unit interval. I took suggested steps from my lecture but I'm not sure if I did it correctly.

According to my lecture the function has to be odd and also periodic. Therefore I extended it according to the notes: F:[−1,1]

F(x)=⎧⎩⎨f(x)0−f(−x)if 0<x≤Lif x=0∨x=Lif −L≤x<0

with F(x+2L)=F(x)