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an infinite trigonometric series of the form 1/ 2 a 0 + a 1 cos x + b 1 sin x + a 2 cos 2 x + b 2 sin 2 x + …, where a 0 , a 1 , b 1 , a 2 , b 2 … are the Fourier coefficients . It is used, esp in mathematics and physics, to represent or approximate any periodic function by assigning suitable values to the coefficients

An infinite series whose terms are constants multiplied by sine and cosine functions and that can, if uniformly convergent, approximate a wide variety of functions.