Several properties of hypergeometric Bernoulli numbers

2018/03/21 by Miho Aoki, Aoki, Miho, Takao Komatsu +3
Mathematics · #05A15 #05A19 #11A55 #11B37 #11B68 #11C20 #15A15 #33C15 #Advanced Mathematical Identities #FOS: Mathematics #Mathematical Inequalities and Applications #Mathematical functions and polynomials #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1803.07804

openalex publication_date 2018/03/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we give the determinant expressions of the hypergeometric Bernoulli numbers, and some relations between the hypergeometric and the classical Bernoulli numbers which include Kummer's congruences. By applying Trudi's formula, we have some different expressions and inversion relations. We also determine explicit forms of convergents of the generating function of the hypergeometric Bernoulli numbers, from which several identities for hypergeometric Bernoulli numbers are given.

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