generating function en · NOUN
Etymology
The concept was introduced by French mathematician Abraham de Moivre in 1730.
Meanings
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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.
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 101:2003, Sergei K. Lando (author & translator), Lectures on Generating Functions, American Mathematical Society.
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.
1990, Herbert S. Wilf, generatingfunctionology, Academic Press, page 2:
Forms
| Spelling | Features | Labels | Source |
|---|---|---|---|
| generating functions | Number=Plur | lexicographic |
Hypernyms
Hyponyms
Bell series · exponential generating function · Lambert series · Dirichlet series · ordinary generating function
Relateds
power series · moment-generating function
Translations (12)
fi emäfunktio (formal power series whose coefficients encode a sequence) · pt função geradora (formal power series whose coefficients encode a sequence) · de erzeugende Funktion (formal power series whose coefficients encode a sequence) · es función generatriz (formal power series whose coefficients encode a sequence) · fr fonction génératrice (formal power series whose coefficients encode a sequence) · fr série génératrice (formal power series whose coefficients encode a sequence) · it funzione generatrice (formal power series whose coefficients encode a sequence) · pt função geratriz (formal power series whose coefficients encode a sequence) · bg пораждаща функция (formal power series whose coefficients encode a sequence) · tr akım fonksiyonu (formal power series whose coefficients encode a sequence) · es función generadora (formal power series whose coefficients encode a sequence) · fi generoiva funktio (formal power series whose coefficients encode a sequence)