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The coefficients of cos(nx) and sin(nx) in the Fourier series representing a particular function are called the Fourier coefficients for that function. If we want to have

f(x) = 1 2 a0 + ∞ ∑ n=1  ( an cos(nx) + bn sin(nx) )

in the range [ − π, π] , we need:

an = 1 π ⌠ ⌡ π − π  f(x)cos(nx)dx ,

bn = 1 π ⌠ ⌡ π − π  f(x)sin(nx)dx

for n=1, 2, 3, ...