Fourier series

Fourierseries English right|thumb|The first four partial sums of the Fourier series decomposition of a square wave 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. Noun * en mathematics analysis Any series resulting from the decomposition of a periodic function into terms involving cosines and sines (or, equivalently, complex exponentials). 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. en 2006 K. F. Riley; M. P. Hobson; S. J. Bence Mathematical Methods for Physics and Engineering: A Comprehensive Guide 3rd https://books.google.com.au/books?id=Mq1nlEKhNcsC&pg=PA415&dq=%22Fourier+series%22&hl=en&sa=X&ved=0ahUKEwimo9qN0L_WAhXKrVQKHdEhC6AQ6AEIkQQwWA#v=onepage&q=%22Fourier%20series%22&f=false 415 w:Cambridge University Press Unlike Taylor series, a Fourier series can describe functions that are not everywhere continuous and/or differentiable. Derived terms en Fourier sine series en Fourier cosine series Related terms en Fourier analysis en Fourier integral en Fourier transform Translations series of cosine and sine functions Armenian: hy Ֆուրիեի շարք Asturian: ast serie de Fourier f Catalan: ca sèrie de Fourier f Chinese: Mandarin: cmn 傅立葉級數 Fùlìyè jíshù, cmn 傅里葉級數 Fùlǐyè jíshù Dutch: nl Fourierreeks Finnish: fi Fourier'n sarja French: fr série de Fourier f Galician: gl serie de Fourier f German: de Fourier-Reihe f, de Fourierreihe f Hungarian: hu Fourier-sor Italian: it serie di Fourier f Japanese: ja フーリエ級数 フーリエきゅうすう,fūrie kyūsū Kazakh: kk Фурье қатары Korean: ko 푸리에 급수 Latin: la series Fourieriana f Polish: pl szereg Fouriera m-in Russian: ru ряд Фурье́ m Spanish: es serie de Fourier f Further reading Fourier analysis Fast Fourier transform Fourier transform en Trigonometric functions Curves en eponyms