See generating function in All languages combined, or Wiktionary
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"etymology_text": "The concept was introduced by French mathematician Abraham de Moivre in 1730.",
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{
"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"
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{
"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.",
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{
"text": "2003, Sergei K. Lando (author & translator), Lectures on Generating Functions, American Mathematical Society."
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"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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"word": "Bell series"
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"(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."
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"word": "moment-generating function"
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{
"code": "fi",
"lang": "Finnish",
"sense": "formal power series whose coefficients encode a sequence",
"word": "generoiva funktio"
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{
"code": "fi",
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"code": "pt",
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"word": "akım fonksiyonu"
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],
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"code": "fi",
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{
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"feminine"
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"tags": [
"feminine"
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{
"code": "tr",
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"sense": "formal power series whose coefficients encode a sequence",
"word": "akım fonksiyonu"
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}
Download raw JSONL data for generating function meaning in English (4.6kB)
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.
If you use this data in academic research, please cite Tatu Ylonen: Wiktextract: Wiktionary as Machine-Readable Structured Data, Proceedings of the 13th Conference on Language Resources and Evaluation (LREC), pp. 1317-1325, Marseille, 20-25 June 2022. Linking to the relevant page(s) under https://kaikki.org would also be greatly appreciated.