A note on polyexponential and unipoly Bernoulli polynomials of the second kind

Abstract

In this paper, the authors study the poly-Bernoulli numbers of the second kind, which are defined by using polyexponential functions introduced by Kims. Also by using unipoly function, we study the unipoly Bernoulli numbers of the second kind, which are attached to an arithmetic function. We derive their explicit expressions and some identities involving poly-Bernoulli numbers of the second kind and unipoly Bernoulli numbers of the second kind.

Keywords

• polyexponential function
• unipoly function
• poly-bernoulli numbers of the second kind
• 05a19
• 11b83
• 34a34