The function f(x) is defined on the interval (-Ļ, Ļ). If f(x) is written as a complex Fourier series of the form
f(x) = ā_(n=-ā)^(ā) cāe^(inx)dx,
show that, for all n,
cā = (1)/(2Ļ) ā«_(-Ļ)^(Ļ) f(x)e^(inx)dx
The function f(x) is defined on the interval (-T, T). If f(x) is written as a complex Fourier series of the form
f(x) = ā_(n=-ā)^(ā) Cāe^(inx)dx,
show that, for all n,
1/(2T) ā«_(-T)^(T) Cāxdx