An explicit formula for computing Bernoulli numbers of the second kind in terms of Stirling numbers of the first kind

Abstract

In the paper, the author finds an explicit formula for computing Bernoulli numbers of the second kind in terms of Stirling numbers of the first kind.

5 pages

References in corpus (4)

• An explicit formula for Bell numbers in terms of Stirling numbers and hypergeometric functions
• An explicit formula for Bernoulli polynomials in terms of $r$-Stirling numbers of the second kind
• An integral representation, complete monotonicity, and inequalities of Cauchy numbers of the second kind
• Alternative proofs of a formula for Bernoulli numbers in terms of Stirling numbers

Cited by in corpus (4)

• Two closed forms for the Bernoulli polynomials
• Integral representations and complete monotonicity related to the remainder of Burnside's formula for the gamma function
• An explicit formula for Bernoulli numbers in terms of Stirling numbers of the second kind
• Formulas involving Cauchy polynomials, Bernoulli polynomials, and generalized Stirling numbers