New approach to q-Genocch, Euler numbers and polynomials and their interpolation functions

TL;DR

This paper introduces a novel construction of q-Genocchi and higher order Euler numbers, exploring their relationships with q-Genocchi and Euler polynomials, differing from previous models.

Contribution

It presents a new method for constructing q-Genocchi and Euler numbers of higher order, expanding the understanding of their interrelations.

Findings

New q-Genocchi numbers and higher order Euler numbers constructed

Established relationships between w-q-Euler and w-q-Genocchi polynomials

Different from existing q-Genocchi numbers of Cangul-Ozden-Simsek

Abstract

We give a new construction of q-Genocchi numbers, Euler numbers of higher order, which are different than the q-Genocchi numbers of Cangul-Ozden-Simsek. By using our q-Genoucchi, Euler nimbers of higher order, we can investigate the interesting relationship between w-q-Euler polynomials and w-q-Genocchi polynomials.