Sums of powers of consecutive q-integers

TL;DR

This paper introduces a q-analogue for the sums of powers of positive integers, extending classical results into the realm of q-calculus.

Contribution

It provides a novel q-analogue formulation for sums of powers of consecutive integers, expanding the mathematical framework of q-integers.

Findings

Derived explicit formulas for q-analogues of power sums

Extended classical sum formulas into q-calculus context

Potential applications in combinatorics and number theory

Abstract

We give the q-analogue of the sums of the n-th powers of positive integers up to k-1.