Some New Identities on the (h,q)-Genocchi numbers and polynomials with weight alpha

TL;DR

This paper introduces new identities for (h,q)-Genocchi numbers and polynomials using fermionic p-adic q-integrals and weighted q-Bernstein polynomials, expanding the mathematical understanding of these special functions.

Contribution

The paper presents novel identities for (h,q)-Genocchi numbers and polynomials derived through p-adic q-integrals and weighted q-Bernstein polynomials, offering new tools for their analysis.

Findings

New identities for (h,q)-Genocchi numbers and polynomials

Application of fermionic p-adic q-integrals in deriving identities

Use of weighted q-Bernstein polynomials in the analysis

Abstract

We give some new identities for (h; q)-Genocchi numbers and polynomials by means of the fermionic p-adic q-integral on Zp and the weighted q-Bernstein polynomials.