An integral representation and properties of Bernoulli numbers of the second kind

Abstract

In the paper, the author establishes an integral representation and properties of Bernoulli numbers of the second kind and reveals that the generating function of Bernoulli numbers of the second kind is a Bernstein function on $(0,\infty )$.

9 pages

References in corpus (4)

• An integral representation and properties of Bernoulli numbers of the second kind
• An integral representation, some inequalities, and complete monotonicity of Bernoulli numbers of the second kind
• An integral representation, complete monotonicity, and inequalities of Cauchy numbers of the second kind
• Complete monotonicity of functions involving the $q$-trigamma and $q$-tetragamma functions

Cited by in corpus (10)

• Two closed forms for the Bernoulli polynomials
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• An integral representation and properties of Bernoulli numbers of the second kind
• An integral representation, some inequalities, and complete monotonicity of Bernoulli numbers of the second kind
• Diagonal recurrence relations, inequalities, and monotonicity related to Stirling numbers
• An integral representation, complete monotonicity, and inequalities of Cauchy numbers of the second kind
• An explicit formula for computing Bernoulli numbers of the second kind in terms of Stirling numbers of the first kind
• A ratio of many gamma functions and its properties with applications
• A Note on Some Recent Results for the Bernoulli Numbers of the Second Kind
• Parametric kinds of generalized Apostol-Bernoulli polynomials and their properties