Some identities of symmetry for the generalized Bernoulli numbers and polynomials

TL;DR

This paper explores symmetry identities related to generalized Bernoulli numbers and polynomials using p-adic invariant integrals, revealing new relationships between power sums and these polynomials.

Contribution

It introduces novel symmetry identities for generalized Bernoulli numbers and polynomials derived from properties of p-adic invariant integrals.

Findings

Established identities for Bernoulli numbers and polynomials

Linked power sums with generalized Bernoulli polynomials

Highlighted symmetric properties of p-adic integrals

Abstract

In this paper, by the properties of p-adic invariant integral on Zp, we establish various identities concerning the generalized Bernoulli numbers and polynomials. From the symmetric properties of p-adic invariant integral on Zp, we give some interesting relationship between the power sums and the generalized Bernoulli polynomials.