On the generalized Bernoulli numbers
Donal F. Connon
TL;DR
This paper presents a new expression for generalized Bernoulli numbers using Bernoulli numbers and exponential complete Bell polynomials, providing a novel mathematical relationship.
Contribution
It introduces a formula linking generalized Bernoulli numbers with Bernoulli numbers through Bell polynomials, expanding theoretical understanding.
Findings
Derived an explicit expression for generalized Bernoulli numbers.
Connected Bernoulli numbers with Bell polynomials in a new way.
Enhanced mathematical tools for studying Bernoulli numbers.
Abstract
We derive an expression for the generalized Bernoulli numbers in terms of the Bernoulli numbers involving the (exponential) complete Bell polynomials.
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Taxonomy
TopicsAdvanced Mathematical Identities · Advanced Combinatorial Mathematics · Mathematical functions and polynomials