Carlitz q-Bernoulli numbers and q-Stirling numbers

TL;DR

This paper explores Carlitz q-Bernoulli numbers and q-Stirling numbers, deriving new formulas and relationships between these special q-analogues of classical number sequences.

Contribution

It introduces novel formulas connecting Carlitz q-Bernoulli numbers with q-Stirling numbers, expanding the theoretical understanding of these q-analogues.

Findings

Derived new formulas relating q-Bernoulli and q-Stirling numbers

Established identities involving q-analogues of classical sequences

Enhanced the theoretical framework of q-number theory

Abstract

In this paper we consider carlitz q-Bernoulli numbers and q-stirling numbers of the first and the second kind. From these numbers we derive many interesting formulae associated with q-Bernoulli numbers.