A note on the alternating sums of powers of consecutive q-integers

TL;DR

This paper introduces new q-Euler numbers and polynomials and derives formulas for alternating sums of powers of consecutive q-integers using these constructs, extending Euler's ideas.

Contribution

The paper presents novel q-Euler numbers and polynomials and applies them to derive formulas for alternating sums of powers of q-integers, advancing the understanding of q-analogues.

Findings

New q-Euler numbers and polynomials are constructed.

Formulas for alternating sums of powers of q-integers are derived.

The approach extends classical Euler sum techniques to the q-analogue setting.

Abstract

In this paper we construct a new q-Euler numbers and polynomials. By using these numbers and polynomials, we give the interesting formulae related to alternating sums of powers of consecutive q-integers following an idea due to Euler.