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Bull. Korean Math. Soc. 2018; 55(6): 1909-1920
Online first article June 29, 2018 Printed November 30, 2018
https://doi.org/10.4134/BKMS.b180039
Copyright © The Korean Mathematical Society.
Some properties of the Bernoulli numbers of the second kind and their generating function
Feng Qi, Jiao-Lian Zhao
Tianjin Polytechnic University, Weinan Normal University
In the paper, the authors find a common solution to three series of differential equations related to the generating function of the Bernoulli numbers of the second kind and present a recurrence relation, an explicit formula in terms of the Stirling numbers of the first kind, and a determinantal expression for the Bernoulli numbers of the second kind.
Keywords: Bernoulli number of the second kind, generating function, solution, differential equation, recurrence relation, explicit formula, Stirling number of the first kind, determinantal expression
MSC numbers: Primary 11B68; Secondary 11B37, 11B73, 34A05, 34A30, 34A34
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