Meanings
plural generating functions
- mathematicsA 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.
2003, Sergei K. Lando (author & translator), Lectures on Generating Functions, American Mathematical Society.
2 more examples
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.
1954, George Pólya, Mathematics and Plausible Reasoning, Volume 1: Induction and Analogy in Mathematics, Princeton University Press, page 101Most 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.
1990, Herbert S. Wilf, generatingfunctionology, Academic Press, page 2
Origin
The concept was introduced by French mathematician Abraham de Moivre in 1730.
Full word history & related roots →Translations
Bulgarian пораждаща функция
- пораждаща функция (poraždašta funkcija)formal power series whose coefficients encode a sequence
Finnish generoiva funktio, emäfunktio
- generoiva funktioformal power series whose coefficients encode a sequence
- emäfunktioformal power series whose coefficients encode a sequence
French fonction génératrice, série génératrice
- fonction génératriceformal power series whose coefficients encode a sequence
- série génératriceformal power series whose coefficients encode a sequence
German erzeugende Funktion
- erzeugende Funktionformal power series whose coefficients encode a sequence
Italian funzione generatrice
- funzione generatriceformal power series whose coefficients encode a sequence
Portuguese função geradora, função geratriz
- função geradoraformal power series whose coefficients encode a sequence
- função geratrizformal power series whose coefficients encode a sequence
Spanish función generadora, función generatriz
- función generadoraformal power series whose coefficients encode a sequence
- función generatrizformal power series whose coefficients encode a sequence
Turkish akım fonksiyonu
- akım fonksiyonuformal power series whose coefficients encode a sequence
Cite this entry
generating function. (n.d.). In WatkinsX Dictionary. Retrieved November 3, 2026, from https://dictionary.watkinsx.com/word/generating%20function
“generating function.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/generating%20function. Accessed November 3, 2026.
WatkinsX Dictionary, s.v. “generating function,” accessed November 3, 2026, https://dictionary.watkinsx.com/word/generating%20function.
Source: generating function on Wiktionary, CC BY-SA 4.0.