I have this function to be made into a complex Fourier series f(x)= -1 for -pi<x<0 , f(x)= 3 for 0<x<pi , f(x)=0 for x=0
The period is 2pi
I know that the Fourier transform should be in the form Sum c_{n}e^{inx}
Where c_{n} = (1/2pi)*[integral]e^{-inx }f(x) dx
The integral and the Sum are between -infinity and infinity
The problem I am having is that I cannot think of a generic function of x that satisfies f(x)= -1 for -pi<x<0 and f(x)= 3 for 0<x<pi to apply to the integral. I know I can omit f(x)=0 for x=0 in the integral because f(x)=0 so it does not contribute to the integral.
Can someone help me evaluate this integral?