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    Trigonometric Series

    Illustration

    Illustration

    Alternate names

    Fourier analysis | trigonometric series

    Basic definition

    A Fourier series is an expansion of a periodic function in terms of an infinite sum of sines and cosines.

    Detailed definition

    A Fourier series is an expansion of a periodic function f(x) in terms of an infinite sum of sines and cosines. Fourier series make use of the orthogonality relationships of the sine and cosine functions. The computation and study of Fourier series is known as harmonic analysis and is extremely useful as a way to break up an arbitrary periodic function into a set of simple terms that can be plugged in, solved individually, and then recombined to obtain the solution to the original problem or an approximation to it to whatever accuracy is desired or practical. Examples of successive approximations to common functions using Fourier series are illustrated above.

    Related terms

    Dini's test | Dirichlet Fourier series conditions | Fourier-Bessel series | Fourier cosine series | Fourier-Legendre series | Fourier sine series | Fourier transform | generalized Fourier series | Gibbs phenomenon | harmonic addition theorem | harmonic analysis | lacunary Fourier series | Lebesgue constants | power spectrum | Riesz-Fischer theorem | simple harmonic motion

    Educational grade level

    college level

    Associated person

    Jean-Baptiste-Joseph Fourier

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