generating function
From Wiktionary, the free dictionary
English
[edit ]Etymology
[edit ]The concept was introduced by French mathematician Abraham de Moivre in 1730.
Noun
[edit ]generating function (plural generating functions )
- (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.
- 1954, George Pólya, Mathematics and Plausible Reasoning, Volume 1: Induction and Analogy in Mathematics, Princeton University Press, page 101:
- 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.
- 1990, Herbert S. Wilf, generatingfunctionology, Academic Press, page 2:
- 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.
- 2003, Sergei K. Lando (author & translator), Lectures on Generating Functions , American Mathematical Society.
Usage notes
[edit ]Despite the name, a generating function is not a function. As a formal power series, it is understood that its indeterminate (not a "variable") is never assigned a value and the series is never evaluated. In fact, the series is not even required to converge.
Hypernyms
[edit ]Hyponyms
[edit ]- exponential generating function
- Bell series
- Dirichlet series
- Lambert series
- ordinary generating function
Translations
[edit ]formal power series whose coefficients encode a sequence
- Bulgarian: пораждаща функция f (poraždašta funkcija)
- Finnish: generoiva funktio , emäfunktio
- French: fonction génératrice f, série génératrice (fr) f
- German: erzeugende Funktion f
- Italian: funzione generatrice f
- Portuguese: função geradora f, função geratriz f
- Spanish: función generadora f, función generatriz f
- Turkish: akım fonksiyonu
See also
[edit ]- moment-generating function (probability, statistics)
- power series
Further reading
[edit ]- Examples of generating functions on Wikipedia.Wikipedia
- Polynomial sequence on Wikipedia.Wikipedia
- Generating function transformation on Wikipedia.Wikipedia