Generalized hypergeometric Bernoulli numbers

TL;DR

This paper introduces a new class of Bernoulli numbers generalized via hypergeometric functions and Dirichlet characters, exploring their properties, relations, and explicit expressions.

Contribution

It presents the first systematic study of hypergeometric Bernoulli numbers associated with Dirichlet characters, including their properties and explicit formulas.

Findings

Derived relations and expressions for the generalized hypergeometric Bernoulli numbers.

Established determinant formulas and properties of these numbers.

Provided initial explicit expressions in the appendix.

Abstract

We introduce generalized hypergeometric Bernoulli numbers for Dirichlet characters. We study their properties, including relations, expressions and determinants. At the end in Appendix we derive first few expressions of these numbers.