Exponential Generating Function

Views Updated: Dec 15, 2025

Abbreviation

EGF

Pronunciation

/ˌɛkspoʊˈnɛnʃəl ˈʤɛnərˌeɪtɪŋ ˈfəŋkʃən/

In this paper, we utilize exponential generating function to establish an identical formula describing the relationship between Bernoulli number and Stirling number of the second kind.
A closed form for the exponential generating function of the generalized Cauchy numbers is obtained.
The asymptotic counting formula of ordered Bell numbers is obtained by means of the method and technique of exponential generating function in combinatorial analysis. This asymptotic counting formula approximates the true vaules of ordered Bell numbers in very high precision.
In this paper we give the exponential generating function for labeled Euler graphs having exactly n 2 connected Euler graphs and the k ( k ≥ 2 ) cut vertices distributed only on one 2 connected Euler graph.
A exponential generating function was introduced by using of the method of combinatorial analysis; Two new analysis expressions about stirling number of the second kind were given through iteration by using of orthogonality relations.

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