See Fourier series on Wiktionary
Download JSON data for Fourier series meaning in All languages combined (6.5kB)
{
"etymology_text": "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.",
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"kind": "topical",
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"name": "Trigonometric functions",
"orig": "en:Trigonometric functions",
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"derived": [
{
"word": "Fourier sine series"
},
{
"word": "Fourier cosine series"
}
],
"examples": [
{
"text": "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,\nAs 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."
},
{
"text": "2001, David Cruz-Uribe (translator), Javier Duoandikoetxea Zuazo, Fourier Analysis, [1995, Javier Duoandikoetxea Zuazo, Análisis de Fourier], American Mathematical Society, page 20,\nThere 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."
},
{
"ref": "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",
"text": "Unlike Taylor series, a Fourier series can describe functions that are not everywhere continuous and/or differentiable.",
"type": "quotation"
}
],
"glosses": [
"Any series resulting from the decomposition of a periodic function into terms involving cosines and sines (or, equivalently, complex exponentials)."
],
"id": "en-Fourier_series-en-noun-6r1TIB-x",
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"mathematics",
"mathematics"
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"mathematical analysis",
"mathematical analysis"
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"series",
"series"
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[
"periodic",
"periodic"
],
[
"cosine",
"cosine"
],
[
"sine",
"sine"
],
[
"complex",
"complex"
],
[
"exponential",
"exponential"
]
],
"raw_glosses": [
"(mathematics, mathematical analysis) Any series resulting from the decomposition of a periodic function into terms involving cosines and sines (or, equivalently, complex exponentials)."
],
"related": [
{
"word": "Fourier analysis"
},
{
"word": "Fourier integral"
},
{
"word": "Fourier transform"
}
],
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"mathematical-analysis",
"mathematics",
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"translations": [
{
"code": "hy",
"lang": "Armenian",
"roman": "Furiei šarkʻ",
"sense": "series of cosine and sine functions",
"word": "Ֆուրիեի շարք"
},
{
"code": "cmn",
"lang": "Chinese Mandarin",
"sense": "series of cosine and sine functions",
"word": "傅立葉級數"
},
{
"code": "cmn",
"lang": "Chinese Mandarin",
"roman": "Fùlìyè jíshù",
"sense": "series of cosine and sine functions",
"word": "傅立叶级数"
},
{
"code": "cmn",
"lang": "Chinese Mandarin",
"sense": "series of cosine and sine functions",
"word": "傅里葉級數"
},
{
"code": "cmn",
"lang": "Chinese Mandarin",
"roman": "Fùlǐyè jíshù",
"sense": "series of cosine and sine functions",
"word": "傅里叶级数"
},
{
"code": "nl",
"lang": "Dutch",
"sense": "series of cosine and sine functions",
"word": "Fourierreeks"
},
{
"code": "fi",
"lang": "Finnish",
"sense": "series of cosine and sine functions",
"word": "Fourier’n sarja"
},
{
"code": "fr",
"lang": "French",
"sense": "series of cosine and sine functions",
"tags": [
"feminine"
],
"word": "série de Fourier"
},
{
"code": "de",
"lang": "German",
"sense": "series of cosine and sine functions",
"tags": [
"feminine"
],
"word": "Fourier-Reihe"
},
{
"code": "de",
"lang": "German",
"sense": "series of cosine and sine functions",
"tags": [
"feminine"
],
"word": "Fourierreihe"
},
{
"code": "hu",
"lang": "Hungarian",
"sense": "series of cosine and sine functions",
"word": "Fourier-sor"
},
{
"code": "it",
"lang": "Italian",
"sense": "series of cosine and sine functions",
"tags": [
"feminine"
],
"word": "serie di Fourier"
},
{
"alt": "フーリエきゅうすう,fūrie kyūsū",
"code": "ja",
"lang": "Japanese",
"sense": "series of cosine and sine functions",
"word": "フーリエ級数"
},
{
"code": "kk",
"lang": "Kazakh",
"roman": "Fure qatary",
"sense": "series of cosine and sine functions",
"word": "Фурье қатары"
},
{
"code": "ko",
"lang": "Korean",
"roman": "purie geupsu",
"sense": "series of cosine and sine functions",
"word": "푸리에 급수"
},
{
"code": "la",
"lang": "Latin",
"sense": "series of cosine and sine functions",
"tags": [
"feminine"
],
"word": "series Fourieriana"
},
{
"code": "ru",
"lang": "Russian",
"roman": "rjad Furʹjé",
"sense": "series of cosine and sine functions",
"tags": [
"masculine"
],
"word": "ряд Фурье́"
}
],
"wikipedia": [
"Fourier series",
"Joseph Fourier"
]
}
],
"word": "Fourier series"
}
{
"derived": [
{
"word": "Fourier sine series"
},
{
"word": "Fourier cosine series"
}
],
"etymology_text": "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.",
"forms": [
{
"form": "Fourier series",
"tags": [
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"lang_code": "en",
"pos": "noun",
"related": [
{
"word": "Fourier analysis"
},
{
"word": "Fourier integral"
},
{
"word": "Fourier transform"
}
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{
"text": "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,\nAs 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."
},
{
"text": "2001, David Cruz-Uribe (translator), Javier Duoandikoetxea Zuazo, Fourier Analysis, [1995, Javier Duoandikoetxea Zuazo, Análisis de Fourier], American Mathematical Society, page 20,\nThere 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."
},
{
"ref": "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",
"text": "Unlike Taylor series, a Fourier series can describe functions that are not everywhere continuous and/or differentiable.",
"type": "quotation"
}
],
"glosses": [
"Any series resulting from the decomposition of a periodic function into terms involving cosines and sines (or, equivalently, complex exponentials)."
],
"links": [
[
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"mathematics"
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"periodic",
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"raw_glosses": [
"(mathematics, mathematical analysis) Any series resulting from the decomposition of a periodic function into terms involving cosines and sines (or, equivalently, complex exponentials)."
],
"topics": [
"mathematical-analysis",
"mathematics",
"sciences"
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"wikipedia": [
"Fourier series",
"Joseph Fourier"
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"translations": [
{
"code": "hy",
"lang": "Armenian",
"roman": "Furiei šarkʻ",
"sense": "series of cosine and sine functions",
"word": "Ֆուրիեի շարք"
},
{
"code": "cmn",
"lang": "Chinese Mandarin",
"sense": "series of cosine and sine functions",
"word": "傅立葉級數"
},
{
"code": "cmn",
"lang": "Chinese Mandarin",
"roman": "Fùlìyè jíshù",
"sense": "series of cosine and sine functions",
"word": "傅立叶级数"
},
{
"code": "cmn",
"lang": "Chinese Mandarin",
"sense": "series of cosine and sine functions",
"word": "傅里葉級數"
},
{
"code": "cmn",
"lang": "Chinese Mandarin",
"roman": "Fùlǐyè jíshù",
"sense": "series of cosine and sine functions",
"word": "傅里叶级数"
},
{
"code": "nl",
"lang": "Dutch",
"sense": "series of cosine and sine functions",
"word": "Fourierreeks"
},
{
"code": "fi",
"lang": "Finnish",
"sense": "series of cosine and sine functions",
"word": "Fourier’n sarja"
},
{
"code": "fr",
"lang": "French",
"sense": "series of cosine and sine functions",
"tags": [
"feminine"
],
"word": "série de Fourier"
},
{
"code": "de",
"lang": "German",
"sense": "series of cosine and sine functions",
"tags": [
"feminine"
],
"word": "Fourier-Reihe"
},
{
"code": "de",
"lang": "German",
"sense": "series of cosine and sine functions",
"tags": [
"feminine"
],
"word": "Fourierreihe"
},
{
"code": "hu",
"lang": "Hungarian",
"sense": "series of cosine and sine functions",
"word": "Fourier-sor"
},
{
"code": "it",
"lang": "Italian",
"sense": "series of cosine and sine functions",
"tags": [
"feminine"
],
"word": "serie di Fourier"
},
{
"alt": "フーリエきゅうすう,fūrie kyūsū",
"code": "ja",
"lang": "Japanese",
"sense": "series of cosine and sine functions",
"word": "フーリエ級数"
},
{
"code": "kk",
"lang": "Kazakh",
"roman": "Fure qatary",
"sense": "series of cosine and sine functions",
"word": "Фурье қатары"
},
{
"code": "ko",
"lang": "Korean",
"roman": "purie geupsu",
"sense": "series of cosine and sine functions",
"word": "푸리에 급수"
},
{
"code": "la",
"lang": "Latin",
"sense": "series of cosine and sine functions",
"tags": [
"feminine"
],
"word": "series Fourieriana"
},
{
"code": "ru",
"lang": "Russian",
"roman": "rjad Furʹjé",
"sense": "series of cosine and sine functions",
"tags": [
"masculine"
],
"word": "ряд Фурье́"
}
],
"word": "Fourier series"
}
This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2024-05-09 from the enwiktionary dump dated 2024-05-02 using wiktextract (4d5d0bb and edd475d). The data shown on this site has been post-processed and various details (e.g., extra categories) removed, some information disambiguated, and additional data merged from other sources. See the raw data download page for the unprocessed wiktextract data.
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