Fourier series en · NOUN
Etymology
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.
Meanings
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Any 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 415:1951 [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.
Forms
| Spelling | Features | Labels | Source |
|---|---|---|---|
| Fourier series | Number=Plur | lexicographic |
Deriveds
Fourier sine series · Fourier cosine series
Relateds
Fourier integral · Fourier transform · Fourier analysis
Translations (20)
ja フーリエ級数 (series of cosine and sine functions) · hu Fourier-sor (series of cosine and sine functions) · fr série de Fourier (series of cosine and sine functions) · fi Fourier’n sarja (series of cosine and sine functions) · ca sèrie de Fourier (series of cosine and sine functions) · cmn 傅立葉級數 /傅立叶级数 (series of cosine and sine functions) · cmn 傅里葉級數 /傅里叶级数 (series of cosine and sine functions) · de Fourier-Reihe (series of cosine and sine functions) · la series Fourieriana (series of cosine and sine functions) · es serie de Fourier (series of cosine and sine functions) · it serie di Fourier (series of cosine and sine functions) · gl serie de Fourier (series of cosine and sine functions) · ko 푸리에 급수 (series of cosine and sine functions) · nl Fourierreeks (series of cosine and sine functions) · de Fourierreihe (series of cosine and sine functions) · kk Фурье қатары (series of cosine and sine functions) · pl szereg Fouriera (series of cosine and sine functions) · ru ряд Фурье́ (series of cosine and sine functions) · hy Ֆուրիեի շարք (series of cosine and sine functions) · ast serie de Fourier (series of cosine and sine functions)