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Any series resulting from the decomposition of a periodic function into terms involving cosines and sines (or, equivalently, complex exponentials).
Definition source: English Wiktionary via Wiktextract
Topics: mathematical-analysis, mathematics, sciences
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.
Meaning relationships
Synonyms: none provided
Antonyms: none provided
the sum of a series of trigonometric expressions; used in the analysis of periodic functions
Definition source: Princeton WordNet 3.0
No example sentence was provided for this meaning.
Meaning relationships
Synonyms: none provided
Antonyms: none provided
Broader terms: series
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.
Across languages
Translations
20 source translations are retained for this English entry.
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Armenian:
Ֆուրիեի շարք
(Furiei šarkʻ)
— series of cosine and sine functions
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Asturian:
serie de Fourier
— series of cosine and sine functions
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Catalan:
sèrie de Fourier
— series of cosine and sine functions
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Chinese Mandarin:
傅立葉級數 /傅立叶级数
(Fùlìyè jíshù)
— series of cosine and sine functions
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Chinese Mandarin:
傅里葉級數 /傅里叶级数
(Fùlǐyè jíshù)
— series of cosine and sine functions
-
Dutch:
Fourierreeks
— series of cosine and sine functions
-
Finnish:
Fourier’n sarja
— series of cosine and sine functions
-
French:
série de Fourier
— series of cosine and sine functions
-
Galician:
serie de Fourier
— series of cosine and sine functions
-
German:
Fourier-Reihe
— series of cosine and sine functions
-
German:
Fourierreihe
— series of cosine and sine functions
-
Hungarian:
Fourier-sor
— series of cosine and sine functions
-
Italian:
serie di Fourier
— series of cosine and sine functions
-
Japanese:
フーリエ級数
— series of cosine and sine functions
-
Kazakh:
Фурье қатары
(Fure qatary)
— series of cosine and sine functions
-
Korean:
푸리에 급수
(purie geupsu)
— series of cosine and sine functions
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Latin:
series Fourieriana
— series of cosine and sine functions
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Polish:
szereg Fouriera
— series of cosine and sine functions
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Russian:
ряд Фурье́
(rjad Furʹjé)
— series of cosine and sine functions
-
Spanish:
serie de Fourier
— series of cosine and sine functions
