Some identities of q-Bernoulli polynomials under symmetry group S3

TL;DR

This paper derives new identities for Carlitz q-Bernoulli polynomials using symmetry group S3, based on q-Volkenborn integrals and generating functions, revealing structural properties of these polynomials.

Contribution

It introduces novel identities of q-Bernoulli polynomials under S3 symmetry, expanding understanding of their algebraic and combinatorial properties.

Findings

New identities of q-Bernoulli polynomials under S3 symmetry

Expressions of derivatives via q-Volkenborn integrals

Connections between generating functions and q-power sums

Abstract

In this paper, we give some new identities of Carlitz q-Bernoulli polynomials under symmetry group S 3 . The derivatives of identities are based on the q-Volkenborn integral expression of the generating function for the Carlitz q-Bernoulli polynomials and the q-Volkenborn integral equations that can be expressed as the exponential generating functions for the q-power sums.