Some properties of the Bernoulli numbers of the second kind and their generating function
Bull. Korean Math. Soc. 2018 Vol. 55, No. 6, 1909-1920
Published online June 29, 2018
Printed November 30, 2018
Feng Qi, Jiao-Lian Zhao
Tianjin Polytechnic University, Weinan Normal University
Abstract : 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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