English Dictionary

generating function

名詞

(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.

日本語の意味

数学において、係数が数列を符号化するための一変項形式的冪級数。数列の性質を解析するために、級数の代数的操作により調べる対象となる。 / また、複数の数列や複数の変数を符号化する一般化された形式も指し、応用に応じた形式が存在する。

To study the sequence of partition numbers, the mathematician constructed a generating function whose coefficients encode the sequence as a formal power series in one indeterminate.

分割数の数列を研究するために、その数学者は各係数が一つの不定元の形式べき級数として数列を符号化する生成関数を構成した。

意味（1）

(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.

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.

generating functions （ plural ）