The story
The concept was introduced by French mathematician Abraham de Moivre in 1730.
Etymology from Wiktionary, CC BY-SA 4.0.
generating function
Today it means: 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. Full definition →