See generating function on Wiktionary
{
"etymology_text": "The concept was introduced by French mathematician Abraham de Moivre in 1730.",
"forms": [
{
"form": "generating functions",
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"expansion": "generating function (plural generating functions)",
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"lang_code": "en",
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"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",
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"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",
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"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"
}
{
"etymology_text": "The concept was introduced by French mathematician Abraham de Moivre in 1730.",
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"form": "generating functions",
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}
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"expansion": "generating function (plural generating functions)",
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{
"word": "exponential generating function"
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{
"word": "Bell series"
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{
"word": "Dirichlet series"
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{
"word": "Lambert series"
},
{
"word": "ordinary generating function"
}
],
"lang": "English",
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"pos": "noun",
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"word": "moment-generating function"
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"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."
],
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"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."
],
"topics": [
"mathematics",
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"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"
}
],
"word": "generating function"
}
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This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2024-11-06 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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