Several properties of hypergeometric Bernoulli numbers

Journal of Inequalities and Applications

Takao Komatsu¹  Miho Aoki²  Gopal Krishna Panda³ 

[1] Department of Mathematical Sciences, School of Science, Zhejiang Sci-Tech University;Department of Mathematics, Shimane University;National Institute of Technology;

关键词: Bernoulli numbers;    Hypergeometric Bernoulli numbers;    Hypergeometric functions;    Kummer’s congruence;    Determinants;    Recurrence relations;   

DOI  :  10.1186/s13660-019-2066-y

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown