generating function

Etymology
The concept was introduced by French mathematician in 1730.

Noun

 * 1)  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.
 * 2) * 2003, Sergei K. Lando (author & translator), Lectures on Generating Functions,.
 * 1) * 2003, Sergei K. Lando (author & translator), Lectures on Generating Functions,.
 * 1) * 2003, Sergei K. Lando (author & translator), Lectures on Generating Functions,.

Usage notes
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.

Translations

 * Finnish: generoiva funktio, emäfunktio
 * French: fonction génératrice,
 * German: erzeugende Funktion
 * Italian: funzione generatrice
 * Portuguese: função geradora, função geratriz
 * Spanish: función generadora, función generatriz
 * Turkish: akım fonksiyonu