A trigonometric series is a series in which the terms are trigonometric functions, often expressed in terms of sine and cosine functions. One of the most common forms of a trigonometric series is a Fourier series, which represents a periodic function as a sum of sine and cosine functions.
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A series whose terms are multiples of sines and cosines of integer multiples of a variable. A Fourier series is the special case with coefficients extracted from a specified function by integration.