Fourier series

noun

Any series resulting from the decomposition of a periodic function into terms involving cosines and sines (or, equivalently, complex exponentials).

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Meanings

nounFourier series (plural Fourier series)
  1. mathematical analysisAny series resulting from the decomposition of a periodic function into terms involving cosines and sines (or, equivalently, complex exponentials).

    Unlike Taylor series, a Fourier series can describe functions that are not everywhere continuous and/or differentiable.

    2006, K. F. Riley, M. P. Hobson, S. J. Bence, Mathematical Methods for Physics and Engineering: A Comprehensive Guide, 3rd edition, Cambridge University Press, page 415
    2 more examples

    1951 [Blackie & Son], R. C. H. Young (translator), Konrad Knopp, Theory and Application of Infinite Series, [1947, Konrad Knopp, Theorie und Anwendung der unendlichen Reihen, 4th Edition], 1990, Dover, Unabridged unaltered reprint of 2nd English Edition, page 493, As we have seen (pp. 369—370), the question of the necessary and sufficient conditions under which the Fourier series of an integrable function converges and represents the given function is one which presents very great difficulties.

    2001, David Cruz-Uribe (translator), Javier Duoandikoetxea Zuazo, Fourier Analysis, [1995, Javier Duoandikoetxea Zuazo, Análisis de Fourier], American Mathematical Society, page 20, There are excellent discussions of Fourier series and integrals in Katznelson [10] and Dym and McKean [4]. The book by R. E. Edwards [5] is an exhaustive study of Fourier series from a more modern perspective.

Origin

Named after French mathematician and physicist Joseph Fourier (1768-1830), who pioneered research into such series and their application to problems of heat transfer and vibration.

Full word history & related roots →

Translations

Catalan sèrie de Fourier
  • sèrie de Fourierseries of cosine and sine functions
Chinese Mandarin 傅立葉級數 /傅立叶级数, 傅里葉級數 /傅里叶级数
  • 傅立葉級數 /傅立叶级数 (Fùlìyè jíshù)series of cosine and sine functions
  • 傅里葉級數 /傅里叶级数 (Fùlǐyè jíshù)series of cosine and sine functions
Dutch Fourierreeks
  • Fourierreeksseries of cosine and sine functions
Finnish Fourier’n sarja
  • Fourier’n sarjaseries of cosine and sine functions
French série de Fourier
  • série de Fourierseries of cosine and sine functions
German Fourier-Reihe, Fourierreihe
  • Fourier-Reiheseries of cosine and sine functions
  • Fourierreiheseries of cosine and sine functions
Hungarian Fourier-sor
  • Fourier-sorseries of cosine and sine functions
Italian serie di Fourier
  • serie di Fourierseries of cosine and sine functions
Japanese フーリエ級数
  • フーリエ級数series of cosine and sine functions
Korean 푸리에 급수
  • 푸리에 급수 (purie geupsu)series of cosine and sine functions
Latin series Fourieriana
  • series Fourierianaseries of cosine and sine functions
Polish szereg Fouriera
  • szereg Fourieraseries of cosine and sine functions
Russian ряд Фурье́
  • ряд Фурье́ (rjad Furʹjé)series of cosine and sine functions
Spanish serie de Fourier
  • serie de Fourierseries of cosine and sine functions
Cite this entry
APA

Fourier series. (n.d.). In WatkinsX Dictionary. Retrieved November 2, 2026, from https://dictionary.watkinsx.com/word/Fourier%20series

MLA

“Fourier series.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/Fourier%20series. Accessed November 2, 2026.

Chicago

WatkinsX Dictionary, s.v. “Fourier series,” accessed November 2, 2026, https://dictionary.watkinsx.com/word/Fourier%20series.

Source: Fourier series on Wiktionary, CC BY-SA 4.0.