Bernoulli numbers and sums of powers of integers of higher order

TL;DR

This paper presents a new polynomial expression for higher sums of powers of integers using higher order Bernoulli numbers, providing a novel mathematical framework for these sums.

Contribution

It introduces a new polynomial formulation for sums of powers of integers based on higher order Bernoulli numbers, extending classical methods.

Findings

Derived explicit polynomial expressions for higher power sums

Connected higher order Bernoulli numbers with sums of powers

Enhanced mathematical tools for analyzing sums of integer powers

Abstract

We give an expression of polynomials for higher sums of powers of integers via the higher order Bernoulli numbers.