Fourier Series ( basics )

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



Hello guys,



I have to solve one basic problem, but I got the result twice smaller that it should be. So, I am thinking that I must have missed something basic.

The problem is [tex]f\left(x\right) = 2x-1[/tex] for ##0<x<1##.



I have to find the Fourier coefficients.

I have found [tex]A_n = \frac{2}{\pi^2}\sum \frac{ (-1)^{n} -1 }{n^2}\cos(n\pi x)[/tex]

but the answer says [tex]A_n=\frac{4}{\pi^2}\sum \frac{ (-1)^n -1 }{n^2}\cos(n\pi x)[/tex] and [tex]B_n = -\frac{2}{\pi} \sum \frac{(-1)^n - 1}{n} \sin(n\pi x)[/tex]



Also I am confused about the thing that I can see on some places formulas for An such that [tex]A_n = \frac{1}{L} \int_{-L}^L f(x)\cos\left(\frac{n\pi}{L}x\right)dx[/tex] and on some places it is [tex]\frac{2}{L}\int_{-L}^L f(x) \cos\left(\frac{n\pi x}{2} x\right)dx[/tex] in my case I solved with the second formula and get for ##L - 1/2## and formula for ##An = 4 \int_0^1 (2x - 1)\cos(2n\pi x)dx##, same for ##B_n## but with sin.



Thanks and hope you could understand my question(s)