Bernoulli Number

Views Updated: Dec 15, 2025

Abbreviation

Pronunciation

/bərˈnuli ˈnəmbər/

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.
Several precise expressions involving Stirling numbers as coefficients for the power sum of natural numbers are given. Some new properties of the Stirling number and counting formulae of the Bernoulli number are obtained.
A recurrence formula of the coefficient of the sum of natural numbers power and the calculating formula of Bernoulli Number(BN)
The Relation Between Euler Number and Bernoulli Number(BN) and Their Application
The uniform expression for two kinds of Stirling number and Bernoulli number

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