Several properties of hypergeometric Bernoulli numbers

Abstract

In this paper, we give several characteristics of hypergeometric Bernoulli numbers, including several identities for hypergeometric Bernoulli numbers which the convergents of the continued fraction expansion of the generating function of the hypergeometric Bernoulli numbers entail. We show an analog of Kummer’s congruences in the classical Bernoulli numbers. We also give some determinant expressions of hypergeometric Bernoulli numbers and some relations between the hypergeometric and the classical Bernoulli numbers. By applying Trudi’s formula, we have some different expressions and inversion relations.