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Examples of generating functions : ウィキペディア英語版
Examples of generating functions
The following examples of generating functions are in the spirit of George Pólya, who advocated learning mathematics by doing and re-capitulating as many examples and proofs as possible. The purpose of this article is to present common ways of creating generating functions.
== Worked example A: basics ==
New generating functions can be created by extending simpler generating functions. For example, starting with
:G(1;x)=\sum_^ x^n = \frac
and replacing x with ax, we obtain
:G(1;ax)=\frac = 1+(ax)+(ax)^2+\cdots+(ax)^n+\cdots =\sum_^ a^n x^n = G(a^n;x).

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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