Some identities for degenerate Bernoulli numbers of the second kind

2018/04/26 by Taekyun Kim, Kim, Taekyun, Dae San Kim +1
Mathematics · Computer Science · #Advanced Mathematical Identities #Mathematical functions and polynomials #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1804.10081

Abstract

We introduce the degenerate Bernoulli numbers of the second kind as a degenerate version of the Bernoulli numbers of the second kind. We derive a family of nonlinear differential equations satisfied by a function closely related to the generating function for those numbers. We obtain explicit expressions for the coefficients appearing in those differential equations and the degenerate Bernoulli numbers of the second kind. In addition, as an application and from those differential equations we have an identity expressing the degenerate Bernoulli numbers of the second kind in terms of those numbers of higher-orders.

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