Symmetric identities on Bernoulli polynomials

TL;DR

This paper generalizes a known identity for Bernoulli polynomials, deriving new symmetric identities that encompass and extend existing results like the Miki identity.

Contribution

It introduces a generalized identity for Bernoulli polynomials and derives new symmetric identities that unify and extend previous known identities.

Findings

Derived a generalized identity for Bernoulli polynomials

Established two new symmetric identities including the Miki identity

Unified several known Bernoulli polynomial identities

Abstract

In this paper, we obtain a generalization of an identity due to Carlitz on Bernoulli polynomials. Then we use this generalized formula to derive two symmetric identities which reduce to some known identities on Bernoulli polynomials and Bernoulli numbers, including the Miki identity.