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Generating function
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== History == Generating functions were first introduced by [[Abraham de Moivre]] in 1730, in order to solve the general linear recurrence problem.<ref>{{cite book |last=Knuth |first=Donald E. |author-link=Donald Knuth |title=Fundamental Algorithms |publisher=Addison-Wesley |year=1997 |isbn=0-201-89683-4 |edition=3rd |series=[[The Art of Computer Programming]] |volume=1 |chapter=§1.2.9 Generating Functions}}</ref> [[George Pólya]] writes in ''[[Mathematics and plausible reasoning]]'': <blockquote>The name "generating function" is due to [[Laplace]]. Yet, without giving it a name, [[Euler]] used the device of generating functions long before Laplace [..]. He applied this mathematical tool to several problems in Combinatory Analysis and the [[Number theory|Theory of Numbers]].</blockquote>
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