Last Updated：2025/12/05

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(mathematics) A formal power series with one indeterminate, whose coefficients are fractions with factorial denominators (of index corresponding to the power of the indeterminate) and numerators which represent a sequence of numbers that is to be studied.

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exponential generating function

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Source Word

exponential generating function

Noun

Japanese Meaning

（数学）指数的生成関数とは、1つの不定元を持つ形式的冪級数であり、各係数は、その不定元の冪に対応する階乗で割られた分数の形を取り、各分子は解析対象となる数列の項を表す。

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To study the number of labelled trees on n vertices, combinatorialists often consider the exponential generating function whose coefficients are the terms of the sequence divided by factorials.

Google Translation / DeepL Translation

n頂点のラベル付き木の個数を調べるため、組合せ論者はしばしば、その係数が階乗で割られた項からなる一変数の形式的べき級数、すなわち指数生成関数を考える。

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