See generating function in All languages combined, or Wiktionary
{ "etymology_text": "The concept was introduced by French mathematician Abraham de Moivre in 1730.", "forms": [ { "form": "generating functions", "tags": [ "plural" ] } ], "head_templates": [ { "args": {}, "expansion": "generating function (plural generating functions)", "name": "en-noun" } ], "lang": "English", "lang_code": "en", "pos": "noun", "senses": [ { "categories": [ { "kind": "other", "name": "English entries with incorrect language header", "parents": [ "Entries with incorrect language header", "Entry maintenance" ], "source": "w" }, { "kind": "other", "name": "Entries with translation boxes", "parents": [], "source": "w" }, { "kind": "other", "name": "Pages with 1 entry", "parents": [], "source": "w" }, { "kind": "other", "name": "Pages with entries", "parents": [], "source": "w" }, { "kind": "other", "name": "Terms with Finnish translations", "parents": [], "source": "w" }, { "kind": "other", "name": "Terms with French translations", "parents": [], "source": "w" }, { "kind": "other", "name": "Terms with German translations", "parents": [], "source": "w" }, { "kind": "other", "name": "Terms with Italian translations", "parents": [], "source": "w" }, { "kind": "other", "name": "Terms with Portuguese translations", "parents": [], "source": "w" }, { "kind": "other", "name": "Terms with Spanish translations", "parents": [], "source": "w" }, { "kind": "other", "name": "Terms with Turkish translations", "parents": [], "source": "w" }, { "kind": "topical", "langcode": "en", "name": "Mathematics", "orig": "en:Mathematics", "parents": [ "Formal sciences", "Sciences", "All topics", "Fundamental" ], "source": "w" } ], "examples": [ { "ref": "1954, George Pólya, Mathematics and Plausible Reasoning, Volume 1: Induction and Analogy in Mathematics, Princeton University Press, page 101:", "text": "A generating function is a device somewhat similar to a bag. Instead of carrying many little objects detachedly, which could be embarrassing, we put them all in a bag, and then we have only one object to carry, the bag.", "type": "quote" }, { "ref": "1990, Herbert S. Wilf, generatingfunctionology, Academic Press, page 2:", "text": "Most often generating functions arise from recurrence formulas. Sometimes, however, from a generating function you will find a new recurrence formula, not the one you started with, that gives new insights into the nature of your sequence.", "type": "quote" }, { "text": "2003, Sergei K. Lando (author & translator), Lectures on Generating Functions, American Mathematical Society." } ], "glosses": [ "A formal power series with one indeterminate, whose coefficients encode a sequence that can be studied by algebraic manipulation of the series; any one of several generalizations, such as to encode more than one sequence or use more than one indeterminate." ], "hypernyms": [ { "word": "formal power series" } ], "hyponyms": [ { "word": "exponential generating function" }, { "word": "Bell series" }, { "word": "Dirichlet series" }, { "word": "Lambert series" }, { "word": "ordinary generating function" } ], "id": "en-generating_function-en-noun-7moZVDyZ", "links": [ [ "mathematics", "mathematics" ], [ "formal power series", "formal power series" ], [ "indeterminate", "indeterminate" ], [ "coefficient", "coefficient" ] ], "raw_glosses": [ "(mathematics) A formal power series with one indeterminate, whose coefficients encode a sequence that can be studied by algebraic manipulation of the series; any one of several generalizations, such as to encode more than one sequence or use more than one indeterminate." ], "related": [ { "topics": [ "probability", "mathematics", "sciences", "statistics", "mathematics", "sciences" ], "word": "moment-generating function" }, { "word": "power series" } ], "topics": [ "mathematics", "sciences" ], "translations": [ { "code": "fi", "lang": "Finnish", "sense": "formal power series whose coefficients encode a sequence", "word": "generoiva funktio" }, { "code": "fi", "lang": "Finnish", "sense": "formal power series whose coefficients encode a sequence", "word": "emäfunktio" }, { "code": "fr", "lang": "French", "sense": "formal power series whose coefficients encode a sequence", "tags": [ "feminine" ], "word": "fonction génératrice" }, { "code": "fr", "lang": "French", "sense": "formal power series whose coefficients encode a sequence", "tags": [ "feminine" ], "word": "série génératrice" }, { "code": "de", "lang": "German", "sense": "formal power series whose coefficients encode a sequence", "tags": [ "feminine" ], "word": "erzeugende Funktion" }, { "code": "it", "lang": "Italian", "sense": "formal power series whose coefficients encode a sequence", "tags": [ "feminine" ], "word": "funzione generatrice" }, { "code": "pt", "lang": "Portuguese", "sense": "formal power series whose coefficients encode a sequence", "tags": [ "feminine" ], "word": "função geradora" }, { "code": "pt", "lang": "Portuguese", "sense": "formal power series whose coefficients encode a sequence", "tags": [ "feminine" ], "word": "função geratriz" }, { "code": "es", "lang": "Spanish", "sense": "formal power series whose coefficients encode a sequence", "tags": [ "feminine" ], "word": "función generadora" }, { "code": "es", "lang": "Spanish", "sense": "formal power series whose coefficients encode a sequence", "tags": [ "feminine" ], "word": "función generatriz" }, { "code": "tr", "lang": "Turkish", "sense": "formal power series whose coefficients encode a sequence", "word": "akım fonksiyonu" } ], "wikipedia": [ "Abraham de Moivre", "generating function" ] } ], "word": "generating function" }
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This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2024-11-06 from the enwiktionary dump dated 2024-10-02 using wiktextract (fbeafe8 and 7f03c9b). 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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